Question
Determine the point on z-axis which is equidistant from the points (1, 5, 7) and (5, 1, -4).
Let P(0, 0, z) be the equidistant from Q(1, 5, 7) and R(5, 1, -4).
So
(PQ)2 = (PR)2 ⇒ (0 - 1)2 + (0 - 5)2 + (z - 7)2 = (0 - 5) + (0 - 1)2 + (z + 4)2
⇒ 1 + 25 + (z - 7)2 = 25 + 1 + (z + 4)2
⇒ 26 + z2 + 49 - 14z = 26 + z2 + 8z + 16
⇒ -14z - 8z = 16 - 49
⇒ -22z = -33
$\Rightarrow\text{z}=\frac{-33}{-22}$
$\Rightarrow\text{z}=\frac{3}{2}$
Required point $=\Big(0,\ 0,\ \frac{3}{2}\Big)$
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.