Grade 9 / Homothety 25 exercises (100% corrected)

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O O OPQC0C6C3C2C1C4C5 ABCOC ABCDO 1. Introduction to homotheties E.9304 Consider the point O and the ten aircraft images shown below : Circle the two planes that are images of each other by a ho-mothety of center O . E.9305 Consider the point O and the ten aircraft images shown below : Circle the two planes that are images of each other by a ho-mothety of center O . E.6860 Shown below are 6 cups of coffee obtained by homothetizing the C 0 cup : 1 Note C 1 the cup obtained by homothety of the cup C 0 of center O and ratio 2 2 Note C 2 the cup obtained by homothety of the cup C 0 of center O and ratio 0.4 3 Note C 3 the cup obtained by homothety of the cup C 0 of center O and ratio 0.6 4 Note C 4 the cup obtained by homothety of the cup C 0 of center P and ratio 0.4 5 Note C 5 the cup obtained by homothety of the cup C 0 of center P and ratio 2 6 Note C 6 the cup obtained by homothety of the cup C 0 of center Q and ratio 2 E.9303 In the plane, consider the triangle ABC and the points O and C shown below : 1 Justify that the point C is the image of the point C by the homothety of center O and ratio 3 . 2 a Place the point A image of the point A by the ho-mothety of center O and ratio 3 . b Place the point B image of the point B by the homo-thety of center O and ratio 3 . c Draw the triangle A B C image of the triangle ABC by the homothety of center O and ratio 3 . 3 a By measuring the lengths in the figure, determine the approximate values of the following quotients : A B AB ; A C AC ; B C BC b What can be said about the lengths of a figure and its image by a homothety of ratio 3 . 2. Homotheties on a grid E.6859 In the grid below, are represented the parallelogram ABCD and the point O . https://chingmath.fr chapExoCorrec/9304 sacados/9304 O chapExoCorrec/9305 sacados/9305 O chapExoCorrec/6860 sacados/6860 OPQC0C6C3C2C1C4C5 chapExoCorrec/9303 sacados/9303 ABCOC chapExoCorrec/6859 sacados/6859 ABCDO
ABCO EFGO ABCDO OABC Draw the image A B C D of the parallelogram ABCD by the homothety with center O and ratio 4 . E.6858 In the grid below, are represented the triangle ABC and the point O . Construct the image A B C of the triangle ABC by the ho-mothety with center O and ratio 4 . 3. Homothety on a grid - negative ratio E.6864 Consider the triangle EFG and the point O shown below : Construct the triangle E F G image of the triangle EFG by the homothety of center O and ratio − 3 . E.6866 Cet exercise is a multiple-choice questionnaire (QCM) . For each question, only one of the three proposed answers is correct. Indicate the correct answer. A homothety of center A and ratio − 2 is a tranformation that : a enlarge lengths b reduces lengths c preserves lengths E.9301 Consider the quadrilateral ABCD and the point O shown below : Construct the quadrilateral A B C D image of the quadrilat-eral ABCD by the homothety of center O and ratio − 2 . 4. Homotheties on white paper E.6861 Consider the triangle ABC and the point O shown below : https://chingmath.fr chapExoCorrec/6858 sacados/6858 ABCO chapExoCorrec/6864 sacados/6864 EFGO chapExoCorrec/6866 sacados/6866 chapExoCorrec/9301 sacados/9301 ABCDO chapExoCorrec/6861 sacados/6861 OABC
OABCD OABCD 1 Draw the triangle A B C image of the triangle ABC by the homothety of center O and ratio 3 2 Copy and complete the following sentences : a Segment [ A B ] is . . . . . . larger than segment [ AB ] . b The straight lines ( AB ) and ( A B ) are . . . . . . c The angles ∠ BAC and ∠ B A C are . . . . . . E.9306 In the plane, consider the quadrilat-eral ABCD and the point O shown below : Draw the quadrilateral A B C D image of the quadrilateral ABCD by the homothety with center O and ratio 2.5 . E.9307 In the plane, consider the quadrilat-eral ABCD and the point O shown below : Draw the quadrilateral A BCD image of the quadrilateral ABCD by the homothety with center O and ratio − 0.75 . 5. Homothety: search for the center E.11148 Consider the four figures below : Using each time the 2 points highlighted on these figures, jus-tify that the " large "figures are the images of the " small " figures by a homothety. The center of each homothety will be highlighted and the ratio of each homothety will be justified. E.6857 The largest of the dolphins was ob-tained by homothety of the other dolphin : Determine the center and ratio of the homothety. https://chingmath.fr chapExoCorrec/9306 sacados/9306 OABCD chapExoCorrec/9307 sacados/9307 OABCD chapExoCorrec/11148 sacados/11148 chapExoCorrec/6857 sacados/6857
F1F2F3F carréAcarréB EEFG O32AB36o11098765413121120191817161514droite(d E.9302 The largest of the dolphins was ob-tained by homothety of the other dolphin : Determine the center and ratio of the homothety. E.2643 The figure F has undergone three distinct homotheties ; for each of them, determine its center and its homothety ratio: E.9297 Consider the squares A and B shown below : where these two squares have a common vertex, the sides are parallel to each other, the side of the square B measures twice that of the square A . 1 Determine the center M of the homothety of ratio 0.5 transforming the square B into the square A . 2 Determine the center N of the homothety of ratio − 0.5 transforming the square B into the square A . E.9300 In the grid below, are represented the triangle DEF and the point E image of the point E by a homothety of ratio 3 . 1 Determine the center O of the homothety transforming the point E into the point E . 2 Draw the image E F G of the triangle EFG by the ho-mothety of center O and ratio 3 . 6. All transformations E.9296 Consider the following fig-ure, consisting of twenty patterns numbered from 1 to 20 , in which : ∠ AOB = 36 o pattern 11 is the image of pattern 1 by the homothety of center O and ratio 2 . https://chingmath.fr chapExoCorrec/9302 sacados/9302 chapExoCorrec/2643 sacados/2643 F1F2F3F chapExoCorrec/9297 sacados/9297 carréAcarréB chapExoCorrec/9300 sacados/9300 EEFG chapExoCorrec/9296 sacados/9296 O32AB36o11098765413121120191817161514droite(d
ABCDEO1u ABCH Directions: This exercise is a multiple choice quiz (MCQ) . No justification is required. For each question three answers are provided. Only one answer is correct For each question, indicate the correct answer. 1 What is the image of the pattern 20 by the symmetry of axis the line ( d ) ? a le pattern 17 b le pattern 15 c the pattern 12 2 By what rotation is pattern 3 the image of pattern 1 ? a A rotation of center O and angle 36 o ; b A rotation of center O and angle 72 o ; c a rotation of center O and angle 90 o . 3 Is the area of the pattern 11 equal to : a to twice the area of the pattern 1 ; b to 4 times the area of pattern 1 ; c to half the area of the pattern 1 ? E.6862 Consider the figure below : 1 What transformations take the elementary pattern (left) to the pattern shown on the right? 2 Which transformations complete the figure? 7. Homotheties and areas E.6865 Below, consider the point O and the polygon AECD formed by the square ABCD and the right triangle BEC at B . 1 Draw the image A E C D of the polygon AECD by the homothety of center O and ratio 2.5 . 2 a Determine the area of polygons AECD and A E C D . b What is the area magnification factor? What do we notice? E.5677 Consider the triangle ABC shown below : 1 Using the compass and ungraduated ruler, draw the triangle AB C obtained by homothetizing the triangle ABC with ratio 2 . 2 a In the triangle ABC , we have the measures : AB = 3 cm ; CH = 2 cm Determine the measure of the area of the triangle ABC . b Deduce the area of the triangle AB C . https://chingmath.fr chapExoCorrec/6862 sacados/6862 chapExoCorrec/6865 sacados/6865 ABCDEO1u chapExoCorrec/5677 sacados/5677 ABCH
∏gureE∏gureD∏gureC∏gureB∏gureAOABCDE 1uAA ABCDE E.7926 Using dynamic geometry soft-ware, the figure A was constructed. By applying homotheties of center O and different ratios to figure A , the other figures were then obtained. 1 What is the ratio of the homothety of center O that yields the figure C from the figure A ? No justification is ex-pected. 2 The homothety of center O and ratio 3 5 is applied to fig-ure E . What figure do we get? No justification is expected. 3 Which figure has an area four times that of the figure A . 8. Homothety and equations E.11180 On a graduated line, consider the two points A and A below : Point A is the image of point A by a homothety of ratio 3 2 . Determine the distance OA . E.11137 Consider the five points of the plane shown below : 1 Determine the center and ratio of the homothety trans-forming A into C and B into D . 2 Determine the center of the homothety of ratio 3 2 trans-forming point B into point A . 3 Justify that there are no homotheties transforming B into C and D into E . https://chingmath.fr chapExoCorrec/7926 sacados/7926 Asie Juin 2018 ∏gureE∏gureD∏gureC∏gureB∏gureAOABCDE chapExoCorrec/11180 sacados/11180 1uAA chapExoCorrec/11137 sacados/11137 ABCDE