Question

$ABC$ is an isosceles triangle. If the coordinates of the base are $B(1,3)$ and $C(-2,7)$. The vertex $A$ can be

• A. $(1,6)$
• B. $(-1/2,5)$
• C. $(-7,1/6)$
• D. $(5/6,6)$

Answer 1

Answer: (D)

$(5/6,6)$

ABC-Isosceles triangle.

Co-ordinates of base are $B(1,3)$ and $C(-2,7)$

vertex 'A' can be any point on perpendicular bisector of BC, but not 'D'.

Slope of BC$=\frac{7-3}{-2-1}=-\frac{4}{3}$

Slope of Line(L)$=\frac{-1}{(-\frac{4}{3})}=\frac{3}{4}$

Mid-point of BC$-$D$=(\frac{-1}{2},5)$

$L:3x-4y=3(-\frac{1}{2})-4\left(5\right)$

$3x-4y=-\frac{3}{2}-20$

$6x-8y=-3-40$

$6x-8y+43=0$

As, only $(5/6,6)$ satisfies 'L'.

So, 'A' can be $(\frac{5}{6},6)$.