Question

Find the possible value of "a" using the distance formula. (4,-1) and (a,5) with d = 10

Answer 1

Answer:

$a=12\text{ or } -4$

Step-by-step explanation:

The distance formula is given by:

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2$

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:

$10=\sqrt{(a-4)^2+(5-(-1))^2}$

Solve for a. Square both sides and simplify:

$100=(a-4)^2+(6)^2$

Simplify:

$64=(a-4)^2$

Take the square root of both sides. Since we are taking an even root, we will need plus/minus. Hence:

$\pm\sqrt{64}=\pm8=a-4$

Solve for a:

$a-4=8\Rightarrow a=12\text{ or } a-4=-8\Rightarrow a=-4$

So, our two possible points are (12, 5) or (-4, 5).