Question

1. what is the length, to the nearest tenth, of the line segment joining the points (-4, 2) and (146, 52)? a. 141.4 b. 150.5 c. 151.9 d. 158.1

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, $(x_1,y_1)=(-4,2)$ and $(x_2,y_2)=(146,52)$.

Step2: Calculate differences

$x_2 - x_1=146-(-4)=150$ and $y_2 - y_1=52 - 2 = 50$.

Step3: Square the differences

$(x_2 - x_1)^2=150^2 = 22500$ and $(y_2 - y_1)^2=50^2=2500$.

Step4: Sum the squared - differences

$(x_2 - x_1)^2+(y_2 - y_1)^2=22500 + 2500=25000$.

Step5: Calculate the square - root

$d=\sqrt{25000}\approx158.1$.

Answer:

d. 158.1