Q. 57 - Precalculus Enhanced with Graphing Utilities

Question

Find the midpoint of the line segment joining the points P₁ and P₂ .

$P_1=(-5,-3); P_2=(11,9)$

Step-by-Step Solution

Answer

The midpoint of line segment is $\left(3,3\right)$.

Step 1. Given information.

Find the midpoint of the line segment joining the points P₁ and P₂ .

$P_1=(-5,-3); P_2=(11,9)$

Step 2. Midpoint Formula.

The midpoint $M=(x, y)$of the line segment from $P_1= \left(x_1,y_1\right) \mathrm{to} P_2=\left(x_2,y_2\right)$is

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

Step 3. Apply the midpoint formula.

The coordinates (x, y) of the midpoint M are 

$x=\frac{x_1+x_2}{2}=\frac{-5+11}{2}=3 \mathrm{and} y=\frac{y_1+y_2}{2}=\frac{-3+9}{2}=3$

So, Midpoint $M=(x,y)=(3,3)$

Step 4. Conclusion.

The midpoint of the line segment is $(3,3)$.