Chapter 1.1, Problem 59AYU

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

61. $P_1=\left(4,-3\right);P_2=\left(6,\text{ 1}\right)$

To determine

To find: The midpoint of the line segment joining ${\text{P}}_1$ and ${\text{P}}_2$.

Answer to Problem 59AYU

$\left(5,-1\right)$

Explanation of Solution

Given:

${\text{P}}_1=\left(4,-3\right)$ and ${\text{P}}_2=\left(6,1\right)$

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 $x_1\text{ = 4, }{y}_1\text{ = }-3,x_2\text{ = 6}$ and $y_2\text{ = 1}$. Then the coordinates $\left(x\text{, }y\right)$ of the midpoint $\text{M}$ are

$x\text{ = }\frac{x_1+x_2}{2}\text{ = }\frac{4+6}{2}=\frac{10}{2}\text{ = 5}$

$y\text{ = }\frac{y_1+{\text{ y}}_2}{2}\text{= }\frac{-3+1}{2}\text{ = }\frac{-2}{2}\text{ = }-\text{1}$

Therefore the coordinates $\left(x\text{, }y\right)$ of $\text{M = }\left(\text{5, −1}\right)$.