Question

Write the equation of the perpendicuoalr bisector that goes through the line segmet. eith end point of (-10,-8) and (-14,8)

Answer 1

To find the equation of the perpendicular bisector that goes through the line segment with endpoints (-10, -8) and (-14, 8), follow these steps: find the midpoint, find the slope, calculate the negative reciprocal slope, and use the point-slope formula to find the equation.

Step-by-step explanation:

To find the equation of the perpendicular bisector that goes through the line segment with endpoints (-10, -8) and (-14, 8), we can follow these steps:

1. Find the midpoint of the line segment by taking the average of the x-coordinates and the average of the y-coordinates.
2. Find the slope of the line segment by using the formula: slope = (change in y)/(change in x).
3. Since the perpendicular bisector has a negative reciprocal slope, calculate the negative reciprocal of the slope.
4. Use the point-slope formula to find the equation of the perpendicular bisector, using the midpoint coordinates and the negative reciprocal slope.

In this case, the midpoint is (-12, 0) and the slope of the line segment is 8/2 = 4. The negative reciprocal of 4 is -1/4. Using the point-slope formula with the midpoint coordinates and the negative reciprocal slope, we get the equation y = (-1/4)x - 3.