Question

Find x so that the length of the segment joining P1(x, 3) and P2(-1, 4) is square root of 10.

Answer 1

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Answer on Question #56371 – Math – Analytic Geometry

Question

Find $x$ so that the length of the segment joining $P_1(x, 3)$ and $P_2(-1, 4)$ is square root of 10.

Solution

$$\left| P_1 P_2 \right| = \sqrt{10} = \sqrt{(x - (-1))^2 + (3 - 4)^2} = \sqrt{(x + 1)^2 + 1} = \sqrt{10} \Rightarrow$$ $$x^2 + 2x + 1 + 1 = 10$$ $$x^2 + 2x - 8 = 0$$ $$x_{1,2} = \frac{-2 \pm \sqrt{4 + 4 \cdot 8}}{2} = -1 \pm \sqrt{9} = \begin{bmatrix} -2 \\ -4 \end{bmatrix}$$

hence, two answers are possible.

**Answer:** $x_1 = -2$, $x_2 = -4$.