#### Coordinate Geometry Model Question Paper

9th Standard

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Maths

Time : 01:00:00 Hrs
Total Marks : 50
5 x 1 = 5
1. On which quadrant does the point (- 4, 3) lie?

(a)

I

(b)

II

(c)

III

(d)

IV

2. A point on the y-axis is ________________

(a)

(1, 1)

(b)

(6,0)

(c)

(0,6)

(d)

(-1, -1)

3. The centre of a circle is (0, 0). One end point of a diameter is (5, -1), then ______________

(a)

$\sqrt{24}$

(b)

$\sqrt{37}$

(c)

$\sqrt{26}$

(d)

$\sqrt{17}$

4. The point (0, -3) lies on _______________

(a)

+ ve x-axis

(b)

+ ve y-axis

(c)

- ve x-axis

(d)

- ve y-axis

5. The diagonal of a square formed by the points (1, 0), (0, 1), (-1, 0) and (0, - 1) is_______________

(a)

2

(b)

4

(c)

$\sqrt{2}$

(d)

8

6. 5 x 2 = 10
7. If A (10, 11) and B (2 ,3) are the coordinates of end points of diameter of circle. Then find the centre of the circle.

8. Find the coordinates of the point which divides the line segment joining the points (3,1) and (S, 13) internally in the ratio 3 : 5.

9. A car travels, at an uniform speed. At 2pm it is at a distance of 5 km at 6pm it is at a distance of 120 km. Using section formula, find at what distance it will reach 2 midnight.

10. Find the centroid of the triangle whose vertices are (2, -5), (5, 11) and (9,9)

11. If the centroid of a triangle is at (10, -1) and two vertices are (3,2) and (5, -11). Find the third vertex of a triangle.

12. 5 x 3 = 15
13. Read the coordinates of the vertices of the triangle ABC with the following figure.

14. Write the coordinates of quadrilateral PQRS as shown in the following figure.

15. Three vertices of a rectangle are (3, 2), (-4, 2) and (-4, 5). Plot the points and find the coordinates of the fourth vertex.

16. the mid-point formula to show that the mid-point of the hypotenuse of a right angled triangle is equidistant from the vertices (with suitable points).

17. Find the centroid of the triangle whose veritices are A(6,−1), B(8,3) and C(10,−5).

18. 4 x 5 = 20
19. Show that the given points (1, 1), (5, 4), (-2, 5) are the vertices of an isosceles right angled triangle.

20. Show that the point (3, -2), (3, 2), (-1, 2) and (-1, -2) taken in order are the vertices of a square.

21. Find the type of triangle formed by (-1, -1), (1, 1) and ($-\sqrt{13},\sqrt{13}$)

22. Find x such that PQ = QR where P(6, -1) Q (1, 3) and R (x, 8) respectively.