Question

question 20 of 25 what is the distance between the points (22, 27) and (2, -10)? if necessary, round your answer to two decimal places. a. 42.06 units b. 57 units c. 31.13 units d. 37 units

Explanation:

Step1: Identify distance formula

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

Step2: Assign values

Let $(x_1,y_1)=(22,27)$ and $(x_2,y_2)=(2,- 10)$. Then $x_2 - x_1=2 - 22=-20$ and $y_2 - y_1=-10 - 27=-37$.

Step3: Calculate squares

$(x_2 - x_1)^2=(-20)^2 = 400$ and $(y_2 - y_1)^2=(-37)^2 = 1369$.

Step4: Sum squares

$(x_2 - x_1)^2+(y_2 - y_1)^2=400 + 1369=1769$.

Step5: Calculate distance

$d=\sqrt{1769}\approx42.06$.

Answer:

A. 42.06 units