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

Use the distance formula $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Here $x_1=-1,y_1 = - 2,x_2=3,y_2 = 4$. Then $d=\sqrt{(3-(-1))^2+(4 - (-2))^2}=\sqrt{(3 + 1)^2+(4 + 2)^2}=\sqrt{4^2+6^2}=\sqrt{16 + 36}=\sqrt{52}=2\sqrt{13}$.

Step3: Calculate the mid - point

Use the mid - point formula $M=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$. Substitute $x_1=-1,y_1 = - 2,x_2=3,y_2 = 4$ into it. We get $M=(\frac{-1 + 3}{2},\frac{-2+4}{2})=(1,1)$.

Answer:

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