1) graph the points a (3, 2) and b (7, 5). find the midpoint of $overline{ab}$. find the distance of…
1) graph the points a (3, 2) and b (7, 5). find the midpoint of $overline{ab}$. find the distance of $overline{ab}$.
Answer
Explanation:
Step1: Identify coordinates
Let $A(x_1,y_1)=(3,2)$ and $B(x_2,y_2)=(7,5)$
Step2: Calculate midpoint
Use midpoint formula: $\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)$ $\left(\frac{3+7}{2},\frac{2+5}{2}\right)=\left(5,\frac{7}{2}\right)$
Step3: Calculate distance
Use distance formula: $\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$ $\sqrt{(7-3)^2+(5-2)^2}=\sqrt{4^2+3^2}=\sqrt{16+9}=\sqrt{25}=5$
Answer:
Midpoint of $\overline{AB}$: $\boldsymbol{\left(5,\frac{7}{2}\right)}$ Distance of $\overline{AB}$: $\boldsymbol{5}$