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

Question

accessdenied · Answer

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.

anonymous · Answer

so what's the answer?