Chapter 1.1, Problem 58AYU

In Problems 57-64, find the midpoint of the line segment joining the points $P_1$ and $P_2$.

60. $P_1=\left(2,-3\right);P_2=\left(10,\text{ 3}\right)$

To determine

To find: The midpoint of the line segment joining $\text{P}₁$ and $\text{P}₂$.

Answer to Problem 58AYU

$\left(\text{6, 0}\right)$

Explanation of Solution

Given:

$\text{P}₁=\left(2,-3\right)$ and $\text{P}₂=\left(10,3\right)$

Formula used:

Midpoint $\text{=}\text{M}\text{=}\left(x\text{, }y\right)=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$.

Calculation:

Apply the midpoint formula using $x_1=2,y_1=-3,x_2=10$ and $y_2=3.$ Then the coordinates $\left(x\text{, }y\right)$ of the midpoint $\text{M}$ are

$x=\frac{x_1+x_2}{2}=\frac{2_{}+10}{2}=\frac{\text{12}}{\text{2}}=6$

$y=\frac{y_1+y_2}{2}=\frac{-3+3}{2}=\frac{0}{2}=0$

Therefore the coordinates $\left(x\text{, }y\right)$ of $\text{M}\text{=}\text{(6},0)$.