J P Mohindru and Bharat Mohindru Solutions for Chapter: Coordinate Geometry, Exercise 5: FOR ASSESSMENT

Find the coordinates of a point on $x$-axis, which is equidistant from the points $(-3, 4)$ and $(2, 5)$.

Find the coordinates of the point, which divides the line segment joining the points $A(4, -3) \text{and} B(9, 7)$ in the ratio $3:2$ internally.

If the coordinates of the midpoint of the line segment joining the points $A\left(-7, 6\right) \text{and} B\left(9,-10\right)$ is $\left(x, y\right)$. Find the value of $x+y$

If $A(1, 2), B(4, 3), \text{and} C(6, 6)$ are three vertices of a parallelogram $ABCD$, find the coordinates of the fourth vertex $D$.

If the centroid of a triangle $ABC$ whose vertices are $A(2, 2), B(-4, -4) \text{and} C(5, -8)$ is $\left(1, k\right)$, then find the value of $k$

If the centroid of the triangle formed by the points $A\left(a, b\right), B\left(b, c\right) \text{and} C\left(c, a\right)$ is at the origin, then the value of $a+b+c$ is?

If $G(-2, 1)$ is the centroid of a triangle $ABC$ and two of its vertices are $A(1,-6) \text{and} B(-5, 2)$, find the third vertex $C$ of the triangle.

If $\left\{x_1\left(y_2-y_3\right)+x_2\left(y_3-y_1\right)+x_3\left(y_1-y_2\right)\right\}$ has non-zero value, then the points $\mathrm{A}(x_1, y_1), \mathrm{B}(x_2, y_2) \text{and} \mathrm{C}(x_3, y_3)$ are _____. (collinear/non-collinear)