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9. Geometry and Algebra
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Q6 of 23 Page 230

Prove that for any point on the line intersecting the axes in this picture, the sum of the x and y coordinates is 3.

Length of x intercept (a) = 3 units


Length of y intercept (b) = 3 units


According to slope intercept form , the equation of the line is




⇒ x + y = 3


Proved


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4

The x coordinate of a point on the slanted (blue) line in the picture is 3.


i) What is its y coordinate?


ii) What is the slope of the line?


iii) Write the equation of the line.

5

In the picture, ABCD is a square. Prove that for any point on the diagonal BD, the sum of the x and y coordinates is zero.

7

Find the equation of the circle with centre at the org in and radius 5. Write the coordinates of eight points on this circle.

8

Let (x, y) be a point on the circle with the line joining (0, 1) and (2, 3) as diameter. Prove that x2 + y2 – 2x – 4y + 3 = 0. Find the coordinates of the points where this circle cuts the x axis.

Questions · 23
9. Geometry and Algebra
1 2 3 4 1 2 3 4 5 6 1 2 3 4 1 2 3 4 5 6 7 8 9
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