Term 3 Coordinate Geometry Book Back Questions

9th Standard

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Maths

Time : 00:45:00 Hrs
Total Marks : 30
5 x 1 = 5
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. 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

3. 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

4. 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

5. 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)

6. 4 x 2 = 8
7. A(−3,2) , B(3,2) and C(−3,−2) are the vertices of the right triangle, right angled at A. Show that the mid-point of the hypotenuse is equidistant from the vertices.

8. 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.

9. 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.

10. 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.

11. 4 x 3 = 12
12. 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.

13. 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).

14. 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.

15. 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.

16. 1 x 5 = 5
17. 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.