Q. 62 - Precalculus Enhanced with Graphing Utilities

Question

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

$P_1=(a,a); P_2=(0,0)$

Step-by-Step Solution

Answer

The midpoint of line segment is 

Step 1. Given information.

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

$P_1=(a,a); P_2=(0,0)$

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 

$x=\frac{x_1+x_2}{2}=\frac{a+0}{2}=\frac{a}{2} \mathrm{and} y=\frac{y_1+y_2}{2}=\frac{a+0}{2}=\frac{a}{2}$

So, Midpoint $M=(x,y)=(\frac{a}{2},\frac{a}{2})$

Step 4. Conclusion.

The midpoint of the line segment is $\left(\frac{a}{2},\frac{a}{2}\right)$.