CORE Coordinate Geometry and Transformations - New Indian ...

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Representation of a line y = mx + c Recall that an equation of the form ax + by + c = o, where a, b and c are real numbers such that a and b are not both zero, is called a linear equation in two variables x and y. For example 2x + 3y = 6, x–y = -5 are linear equations in two variables. You also know how to represent these equations graphically in the Cartesian plane. For example, for representing 2x + 3y = 6, y= we first find at least two solutions: x 0 3 -3 y 2 0 4 Now we locate (plot) the points (0,2), (3, 0) and (-3, 4) in the Cartesian plane and join them to obtain a line. This line is the graph of given equation, or this line represents of equation. (Fig. 9) Fig.9 20
We can always write a linear equation in two variables in the form y = mx + c For example, the equation 2x + 3y = 6, can be written as y = x + If is of the form y = mx + c, where m = and c = 2. Similarly, x – y = -5 can be written as If is of the form and so on. y = x + 5 y = mx + c, where m = 1 and c = 5 The graph of y = mx + c is a straight line (as it is a linear equation in two variables). m is called the gradient which refers to “steepness” or slope of the line and c is called the y-intercept of the line. As you can see from the above examples, the gradient of a straight line representing 2x + 3y = 6, i.e. y = x + 2 is given by m = and c = y – intercept = 2 (See Fig 9) Similarly, the gradient of the straight line representing x – y = -5, i.e. y = x + 5 is 1 and c = 5 (See Fig 10) 21
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 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 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 76 and 77: SELF ASSESSMENT RUBRIC 9- CONTENT (
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3. Draw any triangle ABC. Find the
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6. The length of line segment obtai
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8. Translate the following as per g
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SELF ASSESSMENT RUBRIC 9- CONTENT (
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STUDENT’S WORKSHEET 11 Post Conte
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STUDENT’S WORKSHEET 12 Post Conte
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