Q (-1, a)
P (3, -2)
distance's formula:
[tex]\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}\text{ }[/tex]So:
[tex]d\text{ = }\sqrt[]{(3+1)^2+(-2-a)^2}\text{ = }4\sqrt[]{5}[/tex][tex]\sqrt[]{16+4+4a+a^2\text{ }}=\text{ 4}\sqrt[]{5}[/tex][tex]\sqrt[]{20+4a+a^2\text{ }}=\text{ 4}\sqrt[]{5}[/tex][tex]20+4a+a^2\text{ = 16 x 5}[/tex][tex]\begin{gathered} 20+4a+a^2\text{ = 80} \\ 20+4a+a^2-\text{ 80 = 0 } \\ -60+4a+a^2\text{ = 0} \\ (a\text{ + 10 )(a - 6) = 0} \\ a\text{ = 6 or a = -10} \end{gathered}[/tex]