M L Aggarwal Solutions for Chapter: Coordinate Geometry, Exercise 7: Chapter Test

Find the ratio in which the point $P$ whose ordinate is $-3$ divides the join of $A\left(-2, 3\right)$ and $B\left(5, \frac{-15}{2}\right)$. Hence, find the coordinates of $P$

State whether the following statement is true or false. Justify your answer

The point $A\left(2, 7\right)$ lies on the perpendicular bisector of the line segment joining the points $P\left(6, 5\right)$ and $Q\left(0, 4\right)$

State whether the following statement is true or false. Justify your answer

Point $P\left(-4, 2\right)$ lies on the line segment joining the points $A\left(-4, 6\right)$ and $B\left(-4, -6\right)$

State whether the following statement is true or false. Justify your answer

Point $P\left(0, 2\right)$ is the point of intersection of $y$-axis and perpendicular bisector of the line segment joining the points $A\left(-1, 1\right)$ and $B\left(3, 3\right)$

State whether the following statement is true or false. Justify your answer

Point $P\left(5, -3\right)$ is one of the two points of trisection of the line segment joining the points $A\left(7, -2\right)$ and $B\left(1, -5\right)$

State whether the following statement is true or false. Justify your answer

Points $A\left(4, 3\right), B\left(6, 4\right), C\left(5, -6\right)$ and $D\left(-3, 5\right)$ taken in order are the vertices of a parallelogram.

State whether the following statement is true or false. Justify your answer

The points $\left(4, 5\right), \left(7, 6\right)$ and $\left(6, 3\right)$ are collinear.

State whether the following statement is true or false. Justify your answer

Points $A\left(3, 1\right), B\left(12, -2\right)$ and $C\left(0, 2\right)$ cannot be the vertices of a triangle.