Question

Answer the questions about the perpendicular bisector below.

Answer 1

Given:

The vertices of a triangle are D(1,5), O(7,-1) and G(3,-1).

To find:

The perpendicular bisector of line segment DO.

Solution:

Midpoint formula:

$Midpoint=\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)$

The midpoint of DO is:

$Midpoint=\left(\dfrac{1+7}{2},\dfrac{5+(-1)}{2}\right)$

$Midpoint=\left(\dfrac{8}{2},\dfrac{4}{2}\right)$

$Midpoint=\left(4,2\right)$

Therefore, the midpoint of DO is (4,2).

Slope formula:

$m=\dfrac{y_2-y_1}{x_2-x_1}$

Slope of DO is:

$m=\dfrac{-1-5}{7-1}$

$m=\dfrac{-6}{6}$

$m=-1$

Therefore, the slope of DO is -1.

We know that the product of slopes of two perpendicular line is -1.

$m_1\times m_2=-1$

$m_1\times (-1)=-1$

$m_1=1$

The slope of perpendicular bisector is 1 and it passes through the point (4,2). So, the equation of the perpendicular bisector of DO is:

$y-y_1=m(x-x_1)$

$y-2=1(x-4)$

$y-2+2=x-4+2$

$y=x-2$

Therefore, the equation of the perpendicular bisector of DO is $y=x-2$.