Question

find the distance and midpoint of the line segment shown in the graph. distance = select midpoint = select question 3

Explanation:

Step1: Identify the endpoints

Let the endpoints be $(-1,-2)$ and $(3,4)$.

Step2: Calculate the distance using the distance formula $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$

$d=\sqrt{(3 - (-1))^2+(4-(-2))^2}=\sqrt{(3 + 1)^2+(4 + 2)^2}=\sqrt{4^2+6^2}=\sqrt{16 + 36}=\sqrt{52}=2\sqrt{13}$

Step3: Calculate the mid - point using the mid - point formula $M=(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$

$M=(\frac{-1+3}{2},\frac{-2 + 4}{2})=(1,1)$

Answer:

distance = $2\sqrt{13}$, midpoint = $(1,1)$