#### Coordinate Geometry Full chapter Material

9th Standard

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Maths

Time : 02:00:00 Hrs
Total Marks : 70
10 x 1 = 10
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. If $P(\frac{a}{3},\frac{b}{2})$is the mid-point of the line segment joining A(−4,3) and B(−2,4) then (a,b) is

(a)

(-9, 7)

(b)

$(-3, \frac{7}{2})$

(c)

(9, -7)

(d)

$(3, -\frac{7}{2})$

3. 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

4. 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

5. The ratio in which the x-axis divides the line segment joining the points (6,4) and (1, −7) is

(a)

2:3

(b)

3:4

(c)

4:7

(d)

4:3

6. 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)

7. The mid-point of the line joining (−a,2b) and (−3a,−4b) is

(a)

(2a,3b)

(b)

(−2a, −b)

(c)

(2a,b)

(d)

(−2a, −3b)

8. 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

9. 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

10. 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)

11. 15 x 2 = 30
12. 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.

13. 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.

14. O(0,0) is the centre of a circle whose one chord is AB, where the points A and B are (8,6) and (10,0) respectively. OD is the perpendicular from the centre to the chord AB. Find the coordinates of the mid-point of OD.

15. The points A(−5,4) , B(−1,−2) and C(5,2) are the vertices of an isosceles rightangled triangle where the right angle is at B. Find the coordinates of D so that ABCD is a square.

16. Show that the line segment joining the mid-points of two sides of a triangle is half of the third side
(Hint: Place triangle ABC in a clever way such that A is (0,0), B is (2a,0) and C to be (2b,2c). Now consider the line segment joining the mid-points of AC and BC. This will make calculations simpler).

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

18. Find the coordinates of the point which divides the line segment joining A(−5,11) and B(4,−7) in the ratio 7:2.

19. 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.

20. 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.

21. A car travels at an uniform speed. At 2 pm it is at a distance of 180 km and at 6pm it is at 360 km. Using section formula, find at what distance it will reach 12 midnight.

22. 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.

23. Find the length of median through A of a triangle whose vertices are A(−1,3), B(1,−1) and C(5,1).

24. The vertices of a triangle are (1,2), (h,−3) and (−4,k). If the centroid of the triangle is at the point (5,−1) then find the value of $\sqrt { { (h+k) }^{ 2 }+{ (h+3) }^{ 2 } }$

25. ABC is a triangle whose vertices are A(3,4), B(−2,−1) and C(5,3) . If G is the centroid and BDCG is a parallelogram then find the coordinates of the vertex D.

26. 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.

27. 5 x 3 = 15
28. 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.

29. 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).

30. 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.

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

32. 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.

33. 3 x 5 = 15
34. 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.

35. Find the coordinates of the point which divides the line segment joining the points (3,5) and (8,−10) internally in the ratio 3:2.

36. 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?