#### Coordinate Geometry Model Question Paper

9th Standard

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Maths

Time : 01:30:00 Hrs
Total Marks : 50
7 x 1 = 7
1. The coordinates of the point C dividing the line segment joining the points P(2,4) and Q(5,7) internally in the ratio 2:1 is

(a)

$(\frac{7}{2},\frac{11}{2})$

(b)

(3,5)

(c)

(4,4)

(d)

(4,6)

2. In what ratio does the point Q(1,6) divide the line segment joining the points P(2,7) and R(−2,3)

(a)

1:2

(b)

2:1

(c)

1:3

(d)

3:1

3. The ratio in which the x-axis divides the line segment joining the points A(a1,b1) and B(a2 ,b2 ) is

(a)

b1 : b2

(b)

−b1 : b2

(c)

a1 : a2

(d)

−a1 : a2

4. If the coordinates of the mid-points of the sides AB, BC and CA of a triangle are (3,4), (1,1) and (2,−3) respectively, then the vertices A and B of the triangle are

(a)

(3,2), (2,4)

(b)

(4,0), (2,8)

(c)

(3,4), (2,0)

(d)

(4,3), (2,4)

5. In what ratio does the y-axis divides the line joining the points (−5,1) and (2,3) internally

(a)

1:3

(b)

2:5

(c)

3:1

(d)

5:2

6. If (1,−2), (3,6), (x,10) and (3,2) are the vertices of the parallelogram taken in order, then the value of x is

(a)

6

(b)

5

(c)

4

(d)

3

7. The centroid of the triangle with vertices (−1,−6), (−2,12) and (9,3) is

(a)

(3,2)

(b)

(2,3)

(c)

(4,3)

(d)

(3,4)

8. 9 x 2 = 18
9. The centre of a circle is (−4,2). If one end of the diameter of the circle is (−3,7) then find the other end.

10. The mid-point of the sides of a triangle are (2,4), (−2,3) and (5,2). Find the coordinates of the vertices of the triangle.

11. The points A(−3,6) , B(0,7) and C(1,9) are the mid-points of the sides DE, EF and FD of a triangle DEF. Show that the quadrilateral ABCD is a parallellogram.

12. Prove that the diagonals of the parallellogram bisect each other. [Hint: Take scale on both axes as 1cm=a units]

13. In what ratio does the point P(2,−5) divide the line segment joining A(−3,5) and B(4,−9) .

14. The line segment joining A(6,3) and B(−1, −4) is doubled in length by adding half of AB to each end. Find the coordinates of the new end points.

15. A line segment AB is increased along its length by 25% by producing it to C on the side of B. If A and B have the coordinates (−2,−3) and (2,1) respectively, then find the coordinates of C.

16. If the centroid of a triangle is at (4,−2) and two of its vertices are (3,−2) and (5,2) then find the third vertex of the triangle.

17. If  $\left( \frac { 3 }{ 2 } ,5 \right) ,\left( 7,\frac { -9 }{ 2 } \right)$and$(\frac{13}{2},\frac{-13}{2})$ are mid-points of the sides of a triangle, then find the centroid of the triangle.

18. 5 x 3 = 15
19. The point (3,−4) is the centre of a circle. If AB is a diameter of the circle and B is (5,−6), find the coordinates of A.

20. If (x,3), (6,y), (8,2) and (9,4) are the vertices of a parallelogram taken in order, then find the value of x and y.

21. Find the points which divide the line segment joining A(−11,4) and B(9,8) into four equal parts.

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

23. If the centroid of a triangle is at (−2,1) and two of its vertices are (1,−6) and (−5,2), then find the third vertex of the triangle.

24. 2 x 5 = 10
25. The mid-points of the sides of a triangle are (5,1), (3,−5) and (−5,−1). Find the coordinates of the vertices of the triangle.

26. What are the coordinates of B if point P(−2,3) divides the line segment joining A(−3,5) and B internally in the ratio 1:6?