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#### Coordinate Geometry Model Question Paper

10th Standard EM

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Maths

Time : 01:00:00 Hrs
Total Marks : 50
4 x 1 = 4
1. The slope of the line which is perpendicular to line joining the points (0, 0) and (–8, 8) is

(a)

–1

(b)

1

(c)

$\frac13$

(d)

-8

2. A straight line has equation 8y = 4x + 21. Which of the following is true

(a)

The slope is 0.5 and the y intercept is 2.6

(b)

The slope is 5 and the y intercept is 1.6

(c)

The slope is 0.5 and the y intercept is 1.6

(d)

The slope is 5 and the y intercept is 2.6

3. When proving that a quadrilateral is a parallelogram by using slopes you must find

(a)

The slopes of two sides

(b)

The slopes of two pair of opposite sides

(c)

The lengths of all sides

(d)

Both the lengths and slopes of two sides

4. (2, 1) is the point of intersection of two lines.

(a)

x - y - 3 = 0; 3 x - y - 7 = 0

(b)

x + y = 3; 3x + y =7

(c)

3x + y =3; x + y = 7

(d)

x + 3y - 3 = 0; x - y - 7 = 0

5. 5 x 2 = 10
6. Find the value of ‘a’ for which the given points are collinear.
(2, 3), (4, a) and (6, –3)

7. Show that the given points are collinear: (-3, -4) , (7, 2) and (12, 5)

8. Find a relation between x and y such that the point (x,y) is equidistant from the points (7, 1) and (3, 5).

9. Show that the points (1, 7), (4, 2), (-1,-1) and (-4,4) are the vertices of a square.

10. If A (-5, 7), B (-4, -5), C (-1, -6) and D (4, 5) are the vertices of a quadrilateral, find the area of the quadrilateral ABCD.

11. 4 x 5 = 20
12. The given diagram shows a plan for constructing a new parking lot at a campus. It is estimated that such construction would cost Rs. 1300 per square feet. What will be the total cost for making the parking lot?

13. Find the coordinates at the points of trisection (i.e. points dividing in three equal parts) of the line segment joining the points A(2, -2) and B(-7, 4).

14. If the points A(6, 1), B(8, 2), C(9, 4) and D(P, 3) are the vertices of a parallelogram, taken in order. Find the value of P.

15. Find the area of a triangle whose vertices are (1, -1), (-4, 6) and (-3, -5).

16. 2 x 8 = 16
17. Find the equation of a line whose intercepts on the x and y axes are given below.
-5, $\frac 34$

18. Find the area of the quadrilateral whose vertices, taken in order, are (-4, -2), (-3, -5), (3, -2) and (2, 3).