Answer:
[tex]a=12\text{ or } -4[/tex]
Step-by-step explanation:
The distance formula is given by:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2[/tex]
We are given the two points (4, -1) and (a, 5). The distance between them is 10.
Let (4, -1) be (x₁, y₁) and let (a, 5) be (x₂, y₂). Substitute:
[tex]10=\sqrt{(a-4)^2+(5-(-1))^2}[/tex]
Solve for a. Square both sides and simplify:
[tex]100=(a-4)^2+(6)^2[/tex]
Simplify:
[tex]64=(a-4)^2[/tex]
Take the square root of both sides. Since we are taking an even root, we will need plus/minus. Hence:
[tex]\pm\sqrt{64}=\pm8=a-4[/tex]
Solve for a:
[tex]a-4=8\Rightarrow a=12\text{ or } a-4=-8\Rightarrow a=-4[/tex]
So, our two possible points are (12, 5) or (-4, 5).
