Grade 7 / Relative numbers and locators 51 exercises corrected

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ChingQuizz : 2 exercises available for Quizz assessment : 1. Graduated line: reading coordinates E.11355 Definition: A graduated line is a line that has : an origin (a point) a unit (a length) un positive direction We say that the point A has x-coordinate − 3 and we denote it by A − 3 . Consider the graduated line below : 1 Give the x-coordinates of points B , C , and D . 2 How many units separate points B and C ? E.11356 1 Using a calculator, give the decimal values of the divi-sions : a 1 ÷ 2= ::: b 1 ÷ 4= ::: c 1 ÷ 5= ::: d 1 ÷ 10= ::: Consider the four graduated lines below : 2 Give the x-coordinates of the points A , C , E , G . 3 Place the following points : B − 0 ; 5 on the line ( d 1 ) D 1 ; 25 on the line ( d 2 ) F − 0 ; 8 on the right ( d 3 ) H 1 ; 3 on the right ( d 4 ) E.1287 Give the abscissa of the points A , B , C , and D placed on the scaled line below : E.10732 On the graduated line below, give the abscissas of the points A , B and C : E.1882 Give the abscissae of the points A , B , C and D shown on the line below : E.10731 On the graduated line below, give the abscissas of the points A , B and C : E.10730 On the graduated line below, give the abscissas of the points A , B and C : E.1933 The drawing below represents a grad-uated line whose origin and unit have been erased. We know that the points A and B have abscissas A − 1.4 and B +0.6 , respectively. 1 Place, on the graph above, the origin and unit of the graduated line. 2 Give the abscissas of the points C and D . 2. Graduated line: placing points E.6578 Consider a graduated line and the four points A , B , C and D of this line: 1 Give the abscissae of the four points on the scaled line. 2 Place the following points on the graduated line: E (1.5) ; F ( − 2.7) ; G ( − 0.2) https://chingmath.fr quizzChap/1009 chapExoCorrec/11355 sacados/11355 UnitésUnitésOrigineSens positif-5-4-3-2-1O12345A -5-4-3-2-1O12345BCD chapExoCorrec/11356 sacados/11356 -1O12(d4-1O12(d3-1O12(d2-1O12(d1ACEG chapExoCorrec/1287 sacados/1287 -3-2-1012ABCD chapExoCorrec/10732 sacados/10732 -8-7-6-5-4-3-2-10123BAC chapExoCorrec/1882 sacados/1882 01ABCD chapExoCorrec/10731 sacados/10731 -4-3-2-101234BAC chapExoCorrec/10730 sacados/10730 -2-10123ABC chapExoCorrec/1933 sacados/1933 ABCD chapExoCorrec/6578 sacados/6578 -3-2-1012ABCD
E.1303 Consider a graduated line whose unit is 1 cm and the following three points marked by their abscissas : A abscissa +6 ; B abscissa − 4 ; C abscissa +1 1 What is the measure of segment [ AB ] ? 2 a What is the measure of segment [ CB ] ? b What can be said about the point C relative to the segment [ AB ] . c Construct this graduated line and plot these three points on it. 3 Note x A the abscissa of the point A and x B the abscissa of the point B . Determine the value of x A + x B 2 . What do we notice? 3. Graduated line: construction E.1286 On a graduated line whose unit mea-sures 2 cm , place the points below on the graduated line: A ( − 1.7) ; B (+2.3) ; C ( − 0.5) ; D (+1.4) ; E ( − 3.1) E.10051 Draw a straight line with units of measurement 1 cm and place the following points on this line: H ( − 3 ; 2) ; I (+2 ; 7) ; J (+4 ; 6) ; K ( − 0 ; 9) ; L (+6 ; 4) ; M ( − 2 ; 1) E.10052 Draw a graduated line whose unit measures 1 cm . Then place on this graduated line, the follow-ing points : E (+2.3) ; F ( − 0.7) ; G (+1.6) ; H ( − 2.8) E.10053 Draw a graduated line whose unit measures 3 centimeters. Place the following points on your graduated line: E ( − 2.2) ; F (+1.7) ; G ( − 0.7) 4. Distance to zero E.1271 Definition: On a graduated line, consider a point A . The distance to zero of point A is the distance from point A to the origin of the coordinate system. Consider the graduated line below, on which seven points have been placed : 1 Complete the table below : Point Abscisse Distance from zero A B C D E 2 What can we say about the x-coordinates of points D and E ? E.11357 Definition: Two relative numbers are said to be oppo-sites if they are the same distance from zero but have dif-ferent signs. Consider the graduated line below : 1 a Give the x-coordinate of point A . b Place point B opposite point A . 2 a Give the x-coordinate of point C . b Place point D opposite point C . 5. Graduated line: comparison E.10805 Consider a graduated line and the four points A , B , C , and D on this line: https://chingmath.fr chapExoCorrec/1303 sacados/1303 chapExoCorrec/1286 sacados/1286 chapExoCorrec/10051 sacados/10051 chapExoCorrec/10052 sacados/10052 chapExoCorrec/10053 sacados/10053 chapExoCorrec/1271 sacados/1271 01ABCDE chapExoCorrec/11357 sacados/11357 -3-2-1O123AC chapExoCorrec/10805 sacados/10805 -3-2-1012ABCD
1 Give the x-coordinates of the four points on the gradu-ated line. 2 Place the following points on the graduated line: E ( − 0.2) ; F ( − 2.7) 3 Arrange the six numbers, which are the x-coordinates of these points, in ascending order. 6. Compare relative numbers E.1290 Proposition: to compare : two positive numbers, the largest is the one that is furthest from zero; two negative numbers, the largest is the one closest to zero; two numbers with different signs , the largest is the positive number. Complete this sheet with the signs ˇ < ‘’ and ˇ > ‘’: a − 2 . . . . . . +4 b − 4 . . . . . − 1 c +4 . . . . . . − 2 d +1 . . . . . +7 E.10055 Copy and complete the blanks with the signs < and > : a +2 . . . . . . +5 b +5 . . . . . . -5 c +2 . . . . . . -2 d -5 . . . . . . -101 E.1292 Copy and complete the dotted lines with the symbols < and > : a − 5 ; 3 : : : : : : − 4 ; 7 b +3 ; 7 : : : : : : − 2 ; 1 c − 3 ; 8 : : : : : : − 8 ; 3 d +2 ; 7 : : : : : : − 3 ; 1 E.6594 Copy and complete the dotted lines with the symbols < and > : a -5,4 . . . . . . -6,1 b +1,8 . . . . . . -3,2 c -5,2 . . . . . . -6,3 d +4,8 . . . . . . -1,2 E.1273 Copy and complete the dotted lines with the signs < and > : a -8.4 . . . . . . -8.5 b +2 . . . . . . +12.2 c +15.1 . . . . . . +17.8 d -305.15 . . . . . . -304.149 E.1293 Copy and complete the dotted lines with the symbols < and > : a +2 ; 012 . . . +2 ; 102 b − 6 ; 108 . . . − 6 ; 18 c − 11 ; 93 . . . − 11 ; 903 d +5 ; 94 . . . +5 ; 904 E.10056 Copy and complete the dotted lines with the symbols < and > : a − 1 ; 907 . . . . . . − 1 ; 97 b +125 ; 630 . . . . . +125 ; 71 c − 2 ; 25 . . . . . . +2 ; 205 d − 8 ; 13 . . . . . − 8 ; 123 E.10057 Copy and complete the dotted lines with the symbols < and > : a +2 ; 01 : : : : : : +2 ; 10 b − 7 ; 58 : : : : : : − 7 ; 508 c +5 ; 037 : : : : : : +5 ; 307 d − 201 ; 35 : : : : : : − 201 ; 4 E.11433 Copy and complete the dotted lines with the symbols < and > : a − 5 ; 103 : : : : : : − 5 ; 13 b 7 ; 105 : : : : : : 7 ; 15 c − 4 ; 14 : : : : : : − 4 ; 9 d − 7 ; 17 : : : : : : − 7 ; 475 e 1 ; 72 : : : : : : 1 ; 45 f 8 ; 236 : : : : : : − 8 ; 56 7. Order relative numbers E.10054 Order the following numbers in as-cending order : − 1.25 ; 2.308 ; − 0.5 ; − 1.3 ; 2.45 ; 1.99 E.11432 Order the following numbers in ascending order : 2 ; 402 ; − 3 ; 49 ; − 3 ; 87 ; 2 ; 7 ; − 3 ; 9 ; − 3 ; 807 E.1291 1 What temperature, do we read on the thermome-ter? 2 Consider the following temperatures : +3.6 o C ; − 2.6 o C ; − 1.2 o C ; +1.8 o C ; − 5.8 o C ; +5.2 o C Place these temperatures on the thermometer. 3 Copy and arrange in descending order the tem-peratures from question 2 : 8. Positive coordinate locating https://chingmath.fr chapExoCorrec/1290 sacados/1290 chapExoCorrec/10055 sacados/10055 chapExoCorrec/1292 sacados/1292 chapExoCorrec/6594 sacados/6594 chapExoCorrec/1273 sacados/1273 chapExoCorrec/1293 sacados/1293 chapExoCorrec/10056 sacados/10056 chapExoCorrec/10057 sacados/10057 chapExoCorrec/11433 sacados/11433 chapExoCorrec/10054 sacados/10054 chapExoCorrec/11432 sacados/11432 chapExoCorrec/1291 sacados/1291 -------
E.11189 In a plane equipped with a coordi-nate system, consider the two points A and B : Reading coordinates: A point in the plane is identified using the scale on the two half-lines. We will perform the following two readings in this order : we read the number on the horizontal half-line (x-axis) we read the number on the vertical half-line (y-axis) Point A is identified by the number 14 , then the number 4 . Vocabulary : We say that the point A has coordinates (14 ; 4) L’ x-coordinate of the point A has a value of 14 . L’ ordinate of point A has a value of 4 . 1 Give the coordinates of point B . 2 Place the two points C and D with coordinates : C (2 ; 1) ; D (10 ; 3) Note: Check that points A , B , C , and D are aligned. E.10733 In the plane with a reference point : We have the coordinates : A ( : : : ; : : : ) ; B ( : : : ; : : : ) ; C ( : : : ; : : : ) E.10734 In the plane with a reference point : We have the coordinates : A ( : : : ; : : : ) ; B ( : : : ; : : : ) ; C ( : : : ; : : : ) E.10735 In the plane with a reference point : We have the coordinates : A ( : : : ; : : : ) ; B ( : : : ; : : : ) ; C ( : : : ; : : : ) E.10736 In the plane with a reference point : We have the coordinates : A ( : : : ; : : : ) ; B ( : : : ; : : : ) ; C ( : : : ; : : : ) 9. Locating in the plane with integer coordinates E.6577 We consider the plane with the fol-lowing reference frame : https://chingmath.fr chapExoCorrec/11189 sacados/11189 012468101214124xyAB chapExoCorrec/10733 sacados/10733 0124681012141246xyABC chapExoCorrec/10734 sacados/10734 01234567123xyABC chapExoCorrec/10735 sacados/10735 01231xyABC chapExoCorrec/10736 sacados/10736 012xyABC chapExoCorrec/6577 sacados/6577
1 Give the coordinates of the points A , B , C , and D placed in the above frame. 2 Place the following points in the benchmark : E ( − 3 ; 0) ; F (2 ; − 3) ; G (1 ; 3) ; H (0 ; 2) E.1932 Consider the grid below : 1 Knowing that the point B has coordinate ( − 3 ; − 2) , cor-rectly place the origin the axes of the missing marker. 2 Determine the coordinates of points A , C and D . 3 Among the points placed in this frame : a What is the point with abscissa − 2 ? b What is the point with ordinate − 2 ? E.1883 Consider the reference point in the plane below : 1 Determine the coordinates of the points A , B , C , D and E placed in the above reference frame. 2 Name le (s) point (s) having their abscissa strictly nega-tive. 3 Name le (s) point (s) having their strictly negative ordi-nate. E.1272 Draw a reference frame such that the units of the two axes are each 1 cm . Place the following points in this reference frame : A ( − 6 ; +2) ; B ( − 2 ; +5) ; C (+4 ; +5) D (+6 ; +3) ; E (+10 ; 0) ; F (+10 ; − 2) G (+6 ; − 2) ; H (+6 ; − 4) ; I (+4 ; − 4) J (+4 ; − 2) ; K ( − 2 ; − 2) ; L ( − 2 ; − 4) M ( − 4 ; − 4) ; N ( − 4 ; − 2) ; P ( − 6 ; − 2) Draw the polygon ABCDEFGHIJKLMNP and color its interior. What have you just drawn? 10. Locating in the plane with integer coordinates and geometry E.1894 Consider the following reference frame in the plane : 1 Determine the coordinates of the points B and C . 2 Place points : A ( − 2 ; +1) ; D (0 ; − 2) . 3 What conjecture can be made about the nature of the quadrilateral ABCD ? https://chingmath.fr xxyy-4-3-2-10+1+2+3+4-4-3-2-1+1+2+3+4ABCD chapExoCorrec/1932 sacados/1932 ABDC chapExoCorrec/1883 sacados/1883 -7-6-5-4-3-2-1O+1+2+3+4+5+6-4-3-2-1+1+2+3+4ABCDE chapExoCorrec/1272 sacados/1272 chapExoCorrec/1894 sacados/1894 xxyy-6-5-4-3-2-1O+1+2+3+4+5-3-2-1+1+2BC
E.1289 1 In the reference frame below, place the following points : A ( − 7 ; − 3) ; B ( − 5 ; +2) ; C ( − 2 ; − 1) D (0 ; +4) ; E (+6 ; +6) ; F (+10 ; +4) ; G (+4 ; +2) 2 a Connect the points A , B , C and color the triangle ABC in blue. What is its nature? b Connect the points D , E , F , G and color in red the quadrilateral DEFG . What is its nature? E.6592 We consider, in the plane, the refer-ence frame below : 1 Determine the coordinates of the points A , B and C . 2 Draw the symmetric A B C of the triangle ABC with respect to the point O . 3 Give the coordinates of the points A , B and C . E.1288 1 Place in the frame below the points : A (+2 ; +1) ; B (+4 ; +3) ; C ( − 1 ; +4) Draw the triangle ABC in blue. 2 Draw the symmetrical A of the point A relative to the line ( xx ) . What are the coordinates of the point A ?. Draw, in red, the symmetric of the triangle ABC with respect to ( xx ) . 3 Draw the symmetrical A  of the point A relative to the line ( yy ) . What are the coordinates of the point A  ?. Draw, in green, the symmetric of the triangle ABC with respect to ( yy ) . E.11819 On considère le plan muni d’un repère: 1 Placer les trois points : A ( − 2 ; − 2) ; B (4 ; 2) ; C (6 ; − 1) 2 Conjecturer la nature du triangle ABC . 11. Locating in the plan E.6593 We consider, in the plane, the refer-ence frame below : https://chingmath.fr chapExoCorrec/1289 sacados/1289 0xy chapExoCorrec/6592 sacados/6592 xxyy-6-5-4-3-2-1O+1+2+3+4+5-4-3-2-1+1+2+3ABC chapExoCorrec/1288 sacados/1288 xyxy-5-4-3-2-10+1+2+3+4+5-5-4-3-2-10+1+2+3+4+5 chapExoCorrec/11819 sacados/11819 xxyy-2-101234567-2-112 chapExoCorrec/6593 sacados/6593 xxyy-6-5-4-3-2-1O+1+2+3+4+5-4-3-2-1+1+2+3ADCBEFGHI
1 Determine the coordinates of the points A , B and C . 2 a Name two points with the same abscissa. Give their coordinates. b Name two points with the same y-intercept. Give their coordinates. E.10806 1 Give the coordinates of points A and B given below : 2 Give the coordinates of points C and D given below : 3 Give the coordinates of points E and F given below : E.11434 1 In the plane, consider the coordinate system and the three points shown below : Give the coordinates of points A , B , C . 2 Consider the plane with the coordinate system : Place the three points : D (+4 ; 5 ; +0 ; 5) ; E ( − 3 ; − 1 ; 5) ; F ( − 2.5 ; +1) E.11820 On considère le plan muni d’un repère: 1 Placer les trois points : A ( − 3 ; 0 ; 5) ; B (4 ; 5 ; − 1) ; C (5 ; 1 ; 5) 2 Conjecturer la nature du triangle ABC . E.11821 On considère le plan muni d’un repère: 1 Placer les trois points : A ( − 3 ; 5 ; 1 ; 25) ; B ( − 3 ; 75 ; − 1) ; C (3 ; − 1 ; 75) 2 Conjecturer la nature du triangle ABC . E.11822 On considère le plan muni d’un repère: 1 Placer les trois points : A ( − 5 ; 2) ; B 4 ; − 5 3 ; C 13 3 ; 2 3 2 Conjecturer la nature du triangle ABC . 12. Unclassified exercises E.198 For each question, tick the box corre-sponding to the correct answer: https://chingmath.fr chapExoCorrec/10806 sacados/10806 0-5-4-3-2-1123456789-2-11xyAB 0-3-2-1123-1xyCD 0-3-2-1121xyEF chapExoCorrec/11434 sacados/11434 0-3-2-112-11xyABC 0-5-4-3-2-1123456789-2-11xy chapExoCorrec/11820 sacados/11820 xxyy-3-2-1012345-112 chapExoCorrec/11821 sacados/11821 xxyy-4-3-2-1012345-2-11 chapExoCorrec/11822 sacados/11822 xxyy-5-4-3-2-1012345-2-112 chapExoCorrec/198 sacados/198
a b a = b a <b a > b a 3 − 2 b − 8.3 − 7.9 c 8 3 3 d 28 4 7 e 15 3 16 3 f 8 5 8 6 g 5 17 9 7 E.6431 Complete the comparisons with the signs < and > : a − 3 . . . − 5 b 3 . . . − 2.14 c 2.141 . . . 2.2 d − 3.3 . . . − 3.03 e − 2.5 . . . − 2.75 f 1.103 . . . 1.13 https://chingmath.fr chapExoCorrec/6431 sacados/6431