Answer:
a = ± 2
Step-by-step explanation:
Use the distance formula to calculate XY, then equate to 10
d = [tex]\sqrt{x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]
with (x₁, y₁ ) = X(a -5, - 2a) and (x₂, y₂ ) = Y(a + 1, 2a)
XY = [tex]\sqrt{(a +1-(a-5))^2+(2a-(2a))^2\\}[/tex]
= [tex]\sqrt{(a+1-a+5)^2+(4a)^2}[/tex]
= [tex]\sqrt{6^2+16a^2}[/tex] , then
[tex]\sqrt{36+16a^2}[/tex] = 10 ( square both sides )
36 + 16a² = 100 ( subtract 36 from both sides )
16a² = 64 ( divide both sides by 16 )
a² = 4 ( take the square root of both sides )
a = ± [tex]\sqrt{4}[/tex] = ± 2
