R S Aggarwal and Veena Aggarwal Solutions for Exercise 1: Exercise 6A

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

If the point $P\left(x\mathit{,}\mathit{ }y\right)$ is equidistant from the points $A\left(5, 1\right)$ and $B\left(-1, 5\right)$, prove that $3x=2y$.

 If the point $\left(x\mathit{,}\mathit{ }y\right)$ is equidistant from the points $\left(a+b\mathit{,}\mathit{ }b-a\right)$ and $\left(a-b, a+b\right)$, prove that $bx=ay$.

Show that the following points are the vertices of a rectangle.

$A(-4, -1), B(-2, -4) C(4, 0)$and $D(2, 3)$

Show that the following points are the vertices of a rectangle.

$A(2, -2), B(14, 10) C(11, 13)$ and $D(-1, 1)$

Show that the following points are the vertices of a rectangle.

$A(0, -4), B(6, 2) C(3, 5)$ and $D(-3, -1)$

Show that $\Delta ABC$ with vertices $A(–2, 0), B(0, 2)$ and $C(2, 0)$ is similar to $\Delta DEF$ with vertices $D(–4, 0), F(4, 0)$ and $E(0, 4)$

Show that $\Delta ABC$, where $A(2, 0), B(2, 0), C(0, 2)$ and$\Delta PQR$ where $P(–4, 0), Q(4, 0), R(0, 4)$ are similar triangles