Question

Create the equation of the perpendicular bisector of ab, a(-4, 4) and b(4, 8) in slope intercept form.

Answer 1

The equation of the perpendicular bisector of the line segment with endpoints A(-4, 4) and B(4, 8) is y = -2x + 6.

Step-by-step explanation:

To create the equation of the perpendicular bisector of the line segment AB with endpoints A(-4, 4) and B(4, 8), we must follow these steps:

1. Find the midpoint of AB, which will be a point on the bisector.
2. Calculate the slope of AB and then determine the negative reciprocal for the slope of the perpendicular bisector.
3. Use the point-slope form to write the equation of the perpendicular bisector and then convert it to slope-intercept form.

First, we calculate the midpoint (M) of AB, which is ((-4+4)/2, (4+8)/2) = (0, 6).

Next, the slope of AB is (8-4)/(4-(-4)) = 4/8 = 0.5. The negative reciprocal of 0.5 is -2, since -2 * 0.5 = -1.

Now, we write the equation of the line with slope -2 that passes through point M in point-slope form: y - 6 = -2(x - 0).

Simplifying this into slope-intercept form, we get the equation of the perpendicular bisector: y = -2x + 6.