Question

If Q(0, 2) is equidistant from P(5, −3) and R(x, 7), then find the value(s) of x.

Answer 1

Given, Q(0, 2) is equidistant from P(5, −3) and R(x, 7), which means PQ = QR.

Find the distance of PQ and QR using distance formula,

`sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2)`

PQ = `sqrt((5 - 0)^2 + (-3 -2)^2)`

= `5sqrt2`

QR = `sqrt((0 - x)^2 + (2 - 7)^2)`

= `sqrt(x^2 + 25)`

Now, PQ = QR

∴ `5sqrt2 = sqrt(x^2 + 25)`

On squaring both sides of the above equation, we get

∴ 50 = x² + 25

∴ x² = 25

∴ x = ±5

Therefore, the values of x are 5 and −5.