J P Mohindru and Bharat Mohindru Solutions for Chapter: Coordinate Geometry, Exercise 1: EXERCISE

Find the distance between the points $\left(a{m}_1, \frac{a}{m_1}\right) \text{and} \left(a{m}_2, \frac{a}{m_2}\right)$.

Find the distance between $\left(a\sin \alpha ,-b\cos \alpha \right) \text{and} \left(-a\cos \alpha , b\sin \alpha \right)$ when $\mathrm{a}=1, \mathrm{b}=1 \mathrm{and} \mathrm{\alpha }=45°$.

Two vertices of an isosceles triangle are $(2, 0), (2, 5)$. Find the third vertex if the length of equal side is $3$.

Find the circumcentre of the triangle whose vertices are $(-2,-3), (-1, 0)$ and $(7,-6)$

Find the angle subtended at the origin by the line segment whose endpoints are $(0, 100) \mathrm{and} (10, 0)$

Find the coordinates of the point equidistant from three given points $\mathrm{A}(5, 3), \mathrm{B}(5,-5)$ and $C(1,-5)$

The coordinates of the point $P$ are $(-3, 2)$. Find the coordinates of the point $Q$ which lies on the line joining $P$ and origin such that $\mathrm{OP}=\mathrm{OQ}$.

Show that the points $A(-5, 6), B(3, 0),$ and $C(9, 8)$ are the vertices of an isosceles right-angled triangle. Calculate its area.