Question

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

$P_1=(3,-4);P_2=(5,4)$

Short answer

The midpoint of line segment is (4,0).

Step-by-step solution

Step 1. Given information.

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

$P_1=(3,-4);P_2=(5,4)$

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

$x=\frac{x_1+x_2}{2}=\frac{3+5}{2}=4\mathrm{and}y=\frac{y_1+y_2}{2}=\frac{-4+4}{2}=0$

So, Midpoint$M=(x,y)=(4,0)$.

Step 4. Conclusion.

The midpoint of the line segment is$(4,0)$.