Question

CO-ORDINATE GEOMETRY
1. In which quadrant the point P that divides the line segment joining the points A(2,-5) and B(5,2) in the
ratio 2:3 lies
2. If the midpoint of the line segment joining the points P(6,6-2) and Q(-2,4) is (2,-3), find b?
3. Find the area of triangle whose vertices are (1,2), (3,7) and (5,3)?
4. Find the area of the triangle formed by line joining the midpoints of the sides of the triangle, whose
vertices are (0,-1),(2,1) and (0,3)?
5. If the centroid of the triangle formed by (7,x), (7,-6) and (9,10) is at (6,3) then find the value of (x,y)?
6. If A and B are the points (-6,7) and (-1,-5) respectively then find the distance 2 AB?
7. If the distance between the points (4,K) and (1,0) is 5, then what can be the possible values of K?
8. Find the values of x, if A(x,2), B(-3,-4) and C(7,-5) are collinear?
9. Prove that A(2,-1), B(3,4), C(-2,3) and D(-3,-2) are the vertices of a rhombus ABCD. Is it a square?
10. Show that (3,0), (6,4) and (-1,3) are the vertices of a right angled isosceles triangle.
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Answer 1

Step-by-step explanation:

1:

2:3=m:n

by section formula

x = mx+nx1/m+n

x=2(2)+3(5)/2+3

=4+15/5

=4+3

=7

y=my+ny1/m+n

=2(-5)+3(2)/2+3

=(-10)+6/5

=(-2)+6

=4

(x, y) =(7,4)