Question

Write an equation of the line that is perpendicular bisector of the line segment having endpoints of (-4,4) and (0,-6)

Answer 1

Try thinking about what it means to be a perpendicular bisector of a line segment. We would have a line that goes through the midpoint of that segment and is perpendicular to it.
The midpoint is found between two points through the formula:
\[M(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})\]

Since two points can make a line, we can also find the slope of those points. Algebraically, we would find the slope between two points with the formula
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

Perpendicular lines are opposite reciprocals of their perpendicular counterparts. If the line has a slope of 3, the perpendicular line would have slope -1/3.

Then, we can apply this formula with the midpoint and that perpendicular slope to find the equation of the line:
\[ y - y_1 = m(x - x_1)\]

If we use all of these properties together, we can find the equation of the line.

Answer 2

so what's the answer?