Question

Write the equation of the perpendicular bisector of the segment formed by:

(-4, 3) and (8, -3)

Answer 1

The equation of perpendicular bisector is:

`y = 2x-2`

Explanation:

Given the points

• (-4, 3)

• (8, -3)

First, we need to find the midpoint of the points (-4, 3) and (8, -3)

`\mathrm{Midpoint\:of\:}\left(x_1,\:y_1\right),\:\left(x_2,\:y_2\right):\quad \left((x_2+x_1)/(2),\:\:(y_2+y_1)/(2)\right)`

`\left(x_1,\:y_1\right)=\left(-4,\:3\right),\:\left(x_2,\:y_2\right)=\left(8,\:-3\right)`

`=\left((8-4)/(2),\:(-3+3)/(2)\right)`

`=\left(2,\:0\right)`

Thus, the midpoint of the points is: (2, 0)

Now, finding the slope between (-4, 3) and (8, -3)

`\mathrm{Slope}=(y_2-y_1)/(x_2-x_1)`

`\left(x_1,\:y_1\right)=\left(-4,\:3\right),\:\left(x_2,\:y_2\right)=\left(8,\:-3\right)`

`m=-(1)/(2)`

Therefore, the slope m = -1/2

The slope of the line perpendicular to the segment = [-1] / [-1/2] = 2

Using the point-slope form of the equation of the line, the equation of perpendicular bisector is:

`y-y_1=m\left(x-x_1\right)`

where m is the slope of the line

substituting the slope 2 and the point (2, 0)

`y-y_1=m\left(x-x_1\right)`

`y - 0 = 2 (x-2)`

`y = 2x-2`

Therefore, the equation of perpendicular bisector is:

`y = 2x-2`