#### Coordinate Geometry Model Questions

10th Standard EM

Reg.No. :
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Maths

Time : 01:00:00 Hrs
Total Marks : 50
5 x 1 = 5
1. A man walks near a wall, such that the distance between him and the wall is 10 units. Consider the wall to be the Y axis. The path travelled by the man is

(a)

x = 10

(b)

y = 10

(c)

x = 0

(d)

y = 0

2. 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

3. The equation of a line passing through the origin and perpendicular to the line

(a)

7x - 3y + 4 = 0

(b)

3x - 7y + 4 = 0

(c)

3x + 7y = 0

(d)

7x - 3y = 0

4. When proving that a quadrilateral is a trapezium, it is necessary to show

(a)

Two sides are parallel.

(b)

Two parallel and two non-parallel sides.

(c)

Opposite sides are parallel.

(d)

All sides are of equal length.

5. (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

6. 6 x 2 = 12
7. Find the area of the triangle whose vertices are (-3,5) , (5,6) and (5,-2)

8. Show that the points P(-1.5,3), Q(6,-2) , R(-3,4) are collinear.

9. If the area of the triangle formed by the vertices A(-1,2) , B(k,-2) and C(7,4) (taken in order) is 22 sq. units, find the value of k.

10. If the points P(-1, -4), Q (b, c) and R(5, 1) are collinear and if 2b + c = 4, then find the values of b and c.

11. The floor of a hall is covered with identical tiles which are in the shapes of triangles. One such triangle has the vertices at (-3, 2), (-1, -1) and (1, 2). If the floor of the hall is completely covered by 110 tiles, find the area of the floor.

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

13. 6 x 3 = 18
14. What is the slope of a line whose inclination is 300?

15. The line r passes through the points (–2, 2) and (5, 8) and the line θ passes through the points (–8, 7) and (–2, 0). Is the line r perpendicular to θ ?

16. The line p passes through the points (3, - 2), (12, 4) and the line q passes through the points (6, -2) and (12, 2). Is parallel to q ?

17. Show that the points (-2, 5), (6, -1) and (2, 2) are collinear

18. A(1, -2) , B(6, -2), C(5, 1) and D(2, 1) be four points
Find the slope of the line segment (a) AB (b) CD

19. 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).

20. 3 x 5 = 15
21. Find the value of ‘a’ for which the given points are collinear.
(2, 3), (4, a) and (6, –3)

22. You are downloading a song. The percent y (in decimal form) of mega bytes remaining to get downloaded in x seconds is given by y = -0.1x + 1.