CORE Coordinate Geometry and Transformations - New Indian ...

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Reflection (i) Reflection in x-axis Let P (x, y) be a point (See Fig 19). If we consider x-axis as a plane mirror, then image P‟ of the point P will be at the same distance as P is from x-axis, i.e., PM = P‟M. So, the coordinates of P‟ (x‟ , y‟) will be satisfying the conditions x‟ = x y‟ = -y (x, y) (x, -y) We say that P‟ (x, -y) is the reflection of the point P(x, y) in x-axis. Thus, reflection of the point (3, 4) in x-axis will be (3, -4). Similarly, reflection of the point (-4, 3) in the axis will be (-4, -3) and reflection of the point (-2, -5) in x-axis will be (-2, -(-5)) i.e., (-2, 5) and so on. (ii) Reflection in y-axis Fig. 16 If we consider y-axis as a plane mirror, then image P‟ of the point P will be at the same distance as P is from y-axis i.e., PM = MP‟. 32
So, the coordinates of P‟ (x‟, y‟) will given by x‟ = - x y‟ = y (x, y) (-x, y) We say that P‟ (-x, y) is the reflection of the point P(x, y) in y-axis Thus, reflection of the point (-3, -4) in y-axis will be (-3, 4). Similarly, reflection of the point (3, -4) in y-axis will be (-3, -4) and reflection of the point (-2, -5) in y axis is [-(-2), -5)] i.e,. (2, -5) and so on. (iii) Reflection in the line x = constant, say x = a Fig. 17 Clearly x = a is a line parallel to y-axis. (See Fig.21) Let P(x, y) be any point. If we consider line x = a as a plane mirror, the image P‟ of the point P will be at the same distance as P is from the line x = a. i.e., PM = P‟M. So, the coordinates of P‟ (x‟, y‟) will be given by x – a = a – x‟ i.e., x‟ = 2a – x and y‟ = y (x, y) (2a-x, y) 33
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 42 and 43: We say that P‟ (x‟, y‟) = P
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:
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