If A(x, 2), B(2, -1), and AB = 5 units, find the values of x.

1, -5

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-2, 6

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2, -6

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5, -1

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Solution

The correct option is B -2, 6
Given: A(x, 2), B(2, -1), and AB = 5 units

The distance between two points $(x_{1}, y_{1}) a n d (x_{2}, y_{2})$ is given by $\sqrt{(x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2}} .$

AB = $\sqrt{(x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2}}$

5 = $\sqrt{(2 - x)^{2} + (- 1 - 2)^{2}}$

5 = $\sqrt{(2 - x)^{2} + (- 3)^{2}}$
5 = $\sqrt{(2 - x)^{2} + 9}$
25 = $(2 - x)^{2} + 9$
$(2 - x)^{2}$ = 16
2 - x = $\pm 4$
2 - x = 4 and 2 - x = -4
x = -2 and x = 6

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