Question

point e is located at coordinates (-7, -5). point f is located at coordinates (-2, 7). what is the length of $overline{ef}$? 13 units 17 units 21 units 15 units

Explanation:

Step1: Identify the distance - formula

The distance formula 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, $(x_1,y_1)=(-7,-5)$ and $(x_2,y_2)=(-2,7)$.

Step2: Calculate the difference in x - coordinates

$x_2 - x_1=-2-(-7)=-2 + 7 = 5$.

Step3: Calculate the difference in y - coordinates

$y_2 - y_1=7-(-5)=7 + 5 = 12$.

Step4: Substitute into the distance formula

$d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}=\sqrt{5^2+12^2}=\sqrt{25 + 144}=\sqrt{169}$.

Step5: Simplify the square - root

$\sqrt{169}=13$.

Answer:

13 units