Question

Find a point on the y-axis that is equidistant from the points
(4, −4)
and (1, 1).

Answer 1

The point will be (0, y). x is zero because it is on the y-axis. To proceed from here, we use Pythagoras' Theorem.

\[d^{2}=(4-0)^{2}+(-4-y)^{2}\]
\[d^{2}=(1-0)^{2}+(1-y)^{2}\]

These expressions are equal so:
\[y ^{2}+8y+32=y^{2}-2y+2\]
\[y=-3\]

Your point is \[P(0,-3)\]

Answer 2

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