Question

which equation can be used to find the distance between x(-8,1) and y(4,-6)? select all that apply.
□xy = √((-8 - 4)²+(1 - (-6))²)
□xy = √((-8 - 4)²-(1 - (-6))²)
□xy = √((4+(-8))²-((-6)+1)²)
□xy = √((4 - (-8))²+((-6)-1)²)
□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: Analyze first option

For $XY=\sqrt{(-8 - 4)^2+(1-(-6))^2}$, $x_1=-8,x_2 = 4,y_1 = 1,y_2=-6$. Substituting into $d=\sqrt{(x_1 - x_2)^2+(y_1 - y_2)^2}$ gives $\sqrt{(-8 - 4)^2+(1-(-6))^2}$, so this is correct.

Step3: Analyze second option

The formula has a minus sign between the two squared - terms instead of a plus sign. The correct distance formula has addition, so $XY=\sqrt{(-8 - 4)^2-(1-(-6))^2}$ is incorrect.

Step4: Analyze third option

It has a minus sign between the two squared - terms. The correct formula is $d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$ with addition, so $XY=\sqrt{(4+(-8))^2-((-6)+1)^2}$ is incorrect.

Step5: Analyze fourth option

$XY=\sqrt{(4-(-8))^2+((-6)-1)^2}=\sqrt{(4 + 8)^2+(-6 - 1)^2}$, which is in the form of the distance formula $d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$, so this is correct.

Step6: Analyze fifth option

$1-6$ is incorrect as it should be $1-(-6)$. So $XY=\sqrt{(-8 - 4)^2+(1 - 6)^2}$ is incorrect.

Answer:

$\text{XY}=\sqrt{(-8 - 4)^2+(1-(-6))^2}$, $\text{XY}=\sqrt{(4-(-8))^2+((-6)-1)^2}$