Question

Find x if distance between points L(x, 7) and M(1, 15) is 10.

Answer 1

Distance between LM = 10
$$\begin{gathered} \mathrm{LM}=\sqrt{{\left(x-1\right)}^2+{\left(7-15\right)}^2}=10 \\ \Rightarrow \sqrt{{\left(x-1\right)}^2+{\left(-8\right)}^2}=10 \\ \Rightarrow \sqrt{{\left(x-1\right)}^2+64}=100 \end{gathered}$$
Squaring both sides
$$\begin{gathered} {\left(x-1\right)}^2+64=100 \\ \Rightarrow x^2-2x+1+64=100 \\ \Rightarrow x^2-2x-35=0 \\ \Rightarrow x^2-7x+5x-35=0 \\ \Rightarrow x\left(x-7\right)+5\left(x-7\right)=0 \\ \Rightarrow \left(x+5\right)\left(x-7\right)=0 \\ \Rightarrow x=-5,7 \end{gathered}$$