CORE Coordinate Geometry and Transformations - New Indian ...

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We say that P‟ (x‟, y‟) = P‟ (2a-x, y) is the reflection of the point P (x, y) in x = a Thus, reflection of the point (3, 4) in the line x=2 is (2x2 -3, 4) i.e., (1, 4). Similarly, reflection of the point (-2, 3) in the line x = -3 is (2(-3) – (-2), 3) i.e., (-4, 3) and reflection of the point (5, -9) in the line x = 4 is (2 x 4 -5, -9) i.e., (3, -9) and so on. (iv) Reflection in the line y = constant, say, y = b Fig. 18 Clearly, y = b is a line parallel to x axis. (See Fig. 22). Let P(x, y) be any point. If we consider line y = b as a plane mirror, the image P‟ of the point P will be at the same distance as P is from the line y = b i.e., PM = P‟M. So, the coordinates of P‟(x‟, y‟) will be given by x‟ = x y – b = b –y‟, i.e., y‟ = 2b - y (x, y) (x, 2b -y) We say that P‟ (x, 2b –y) is the reflection of the point P(x, y) in the line y = b. Thus, reflection of the point (3, 4) in the line y = 2 is (3, 2 x 2 -4) i.e., (3, 0). 34
Similarly, reflection of the point (-2, 3) in the line y = -4 is (-2, 2 x (-4) – 3), i.e., (-2, -11) and reflection of the point (1, -1) in the line y= -3 is (1, 2 x (-3) – (-1)), i.e., (1, -5) Example10: Find the reflection of C(7, -4) in the ABC formed by the vertices A(5,2), B(4, 7) and (i) (ii) (iii) x-axis, y-axis, Show that reflected triangle obtained in each case is congruent to the original triangle. Solution: (i) Reflection in x-axis A(5, 2) A‟(5, -2) B(4, 7) B‟(4, -7) C(7, -4) C‟(7, 4) A‟ B‟ C‟ is the reflection of ABC in x-axis (ii) Reflection in y-axis A(5, 2) A”(-5, 2) B(4, 7) B”(-4, 7) C(7, -4) C”(-7, -4) A” B” C” is the reflection of ABC in y-axis (iii) Here AB = = A‟ B‟ = = 35
Page 1: CBSE-i CLASS X UNIT-6 CORE Coordina
Page 4 and 5: The CBSE-International is grateful
Page 6 and 7: Advisory Conceptual Framework Shri
Page 8 and 9: vAssessment Plan 4. Study Material
Page 10 and 11: SCOPE DOCUMENT Key concepts/terms:
Page 12 and 13: TEACHER’S NOTE The teaching of Ma
Page 14 and 15: Understand translation as transform
Page 16 and 17: ACTIVITY 1 - WARM UP (W1) (Planting
Page 18 and 19: ACTIVITY 5 -CONTENT (CW1) (Distance
Page 20 and 21: ACTIVITY 9 -CONTENT (CW5) (Transfor
Page 22 and 23: STUDY MATERIAL 14
Page 24 and 25: OX and OY are called the positive d
Page 26 and 27: Thus, points in quadrant I are in t
Page 28 and 29: Representation of a line y = mx + c
Page 30 and 31: Fig. 10 Note that for a given line
Page 32 and 33: Fig. 11 The graph of y = 3x + 3 is
Page 34 and 35: Example 5: Find the distance betwee
Page 36 and 37: 3. Section Formula Consider any two
Page 38 and 39: Solution: Let P(x,y) be the point w
Page 40 and 41: Reflection (i) Reflection in x-axis
Page 44 and 45: Thus, AB = A‟ B‟ Similarly, we
Page 46 and 47: (i) Translation of a line segment P
Page 48 and 49: STUDENT’S SUPPORT MATERIAL 40
Page 50 and 51: SELF ASSESSMENT RUBRIC 1- WARM UP (
Page 52 and 53: STUDENT’S WORKSHEET 3 Pre Content
Page 54 and 55: Take four points in the coordinate
Page 56 and 57: STUDENT’S WORKSHEET 4 Pre Content
Page 58 and 59: STUDENT’S WORKSHEET 5 Content (CW
Page 60 and 61: SELF ASSESSMENT RUBRIC 5- CONTENT (
Page 62 and 63: 5. Plot three points in the coordin
Page 64 and 65: 9. Plot three points in the coordin
Page 66 and 67: 13. Plot four points in the coordin
Page 68 and 69: 17. Plot four points in the coordin
Page 74 and 75: 5. Rama is holding a rope, the end
Page 78 and 79: 3. Draw any triangle ABC. Find the
Page 80 and 81: 6. The length of line segment obtai
Page 82 and 83: 8. Translate the following as per g
Page 86 and 87: STUDENT’S WORKSHEET 11 Post Conte
Page 88 and 89: STUDENT’S WORKSHEET 12 Post Conte
Page 90 and 91: SUGGESTED VIDEOS AND EXTRA READINGS

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