Question

what is the distance between the two endpoints in the graph below? if necessary, round your answer to two decimal places. (5, 6) (-4, -7) a. 16.45 units b. 13 units c. 22 units d. 15.81 units

Explanation:

Step1: Recall 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, $(x_1,y_1)=(-4,-7)$ and $(x_2,y_2)=(5,6)$.

Step2: Calculate differences

$x_2 - x_1=5-(-4)=9$ and $y_2 - y_1=6 - (-7)=13$.

Step3: Square differences and sum

$(x_2 - x_1)^2=9^2 = 81$ and $(y_2 - y_1)^2=13^2 = 169$. Then $(x_2 - x_1)^2+(y_2 - y_1)^2=81 + 169=250$.

Step4: Calculate distance

$d=\sqrt{250}\approx15.81$.

Answer:

D. 15.81 units