Question

which equation can be used to find the distance between x(-8, 1) and y(4, -6)? select all that apply. a xy = √((-8 - 4)²+(1 - (-6))²) b xy = √((4 - (-8))²+((-6) - 1)²) c xy = √((4 + (-8))²-((-6)+1)²) d xy = √((-8 - 4)²+(1 - 6)²) e xy = √((-8 - 4)²-(1 - (-6))²)

Explanation:

Step1: Recall distance formula

The distance $d$ between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Here, $x_1=-8,y_1 = 1,x_2 = 4,y_2=-6$.

Step2: Substitute values into formula

Substituting gives $XY=\sqrt{(4-(-8))^2+((-6)-1)^2}=\sqrt{(4 + 8)^2+(-6 - 1)^2}=\sqrt{12^2+(-7)^2}$. Also, we can write it as $XY=\sqrt{(-8 - 4)^2+(1-(-6))^2}=\sqrt{(-12)^2+(1 + 6)^2}$.

Answer:

A. $XY=\sqrt{(-8 - 4)^2+(1-(-6))^2}$
B. $XY=\sqrt{(4-(-8))^2+((-6)-1)^2}$