Co-ordinate geometry Assignment

Calculate the Following

1. Distance between the point  (1,3) and ( 2,4)
2. Mid-point of line segment  AB where A(2,5) and B( -5,5)
3. Area of  the triangle  formed by joining the line segments (0,0)  ,( 2,0) and (3,0)
4. Distance of point (5,0) from Origin
5. Distance of point (5,-5) from Origin
6. Coordinate of the point M which divided the line segment A(2,3) and B( 5,6) in the ratio 2:3
7. Quadrant of the Mid-point of the line segment A(2,3) and B( 5,6)
8.  the coordinates of a point A, where AB is the diameter of circle whose center is (2,−3) and B is (1, 4)

Find the centroid of the triangle XYZ whose vertices are X (3, – 5) Y (- 3, 4) and Z (9, – 2).
a) (0, 0)
b) (3, 1)
c) (2, 3)
d) (3,-1)

Question 3
The area of the triangle ABC with coordinates as A (1, 2) B (2, 5) and C (- 2, – 5)
a)  -1
b) .4
c)  2
d) 1

Question 4
Find the value of  p for which these point are collinear  (7,-2) , (5,1) ,(3,p)?
a) 2
b) 4
c)  3
d) None of these

Question 5
Determine the ratio in which the line 2x + y – 4 = 0 divides the line segment joining the points A (2, – 2) and B (3, 7).
a) 2:9
b) 1:9
c)1:2
d) 2:3

Question 6
If the mid-point of the line segment joining the points A (3, 4) and
B (a, 4) is P (x, y) and x + y – 20 = 0,then find the value of a
a) 0
b) 1
c) 40
d)  45