JAMB 1998 · UME · Q32

Coordinate geometry

If the distance between the points $(x, 3)$ and $(-x, 2)$ is 5, find $x$ .

Worked solution (try it first)

The changes are $x - (-x) = 2x$ and $3 - 2 = 1$ .
By the distance formula, $(2x)^2 + 1^2 = 5^2$ , so $4x^2 + 1 = 25$ .
Then $4x^2 = 24$ and $x^2 = 6$ .
Take the positive square root: $x = \sqrt6$ , option C.

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