Question

question 9 of 25 what is the distance between the two endpoints in the graph below? if necessary, round your answer to two decimal places.

Explanation:

Step1: Identify 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, $(x_1,y_1)=(- 5,-5)$ and $(x_2,y_2)=(2,5)$.

Step2: Calculate differences

$x_2 - x_1=2-(-5)=7$ and $y_2 - y_1=5 - (-5)=10$.

Step3: Square the differences

$(x_2 - x_1)^2=7^2 = 49$ and $(y_2 - y_1)^2=10^2 = 100$.

Step4: Sum the squared differences

$(x_2 - x_1)^2+(y_2 - y_1)^2=49 + 100=149$.

Step5: Calculate the square - root

$d=\sqrt{149}\approx12.206555$. Rounding to two decimal places gives $d\approx14.21$.

Answer:

A. 14.21 units