Question

determine an equation for the perpendicular bisector of a line segment with the endpoints. c(-2, 0) d(4, -4)

Answer 1

To find the equation of the perpendicular bisector of a line segment with endpoints (-2, 0) and (4, -4), find the midpoint, calculate the slope of the line segment, find the negative reciprocal of the slope, and use the midpoint and slope to write the equation.

Step-by-step explanation:

To determine an equation for the perpendicular bisector of a line segment with endpoints C(-2, 0) and D(4, -4), follow these steps:

1. Find the midpoint of the line segment by averaging the x-coordinates and y-coordinates of the endpoints. The midpoint is M(-2, -2).
2. Find the slope of the given line segment using the slope formula: m = (y2 - y1) / (x2 - x1). The slope of CD is -1/2.
3. Determine the negative reciprocal of the slope of CD to find the slope of the perpendicular line. The negative reciprocal of -1/2 is 2.
4. Use the midpoint and the slope of the perpendicular line to write the equation of the perpendicular bisector. Plugging in the values, we get the equation y + 2 = 2(x + 2).

Therefore, the equation of the perpendicular bisector of CD is y + 2 = 2(x + 2).