Question

find an equation for the perpendicular bisector of the line segment whose endpoints are (9,1) and (-1,5)

Answer 1

The equation of the perpendicular bisector of the line segment with endpoints (9,1) and (-1,5) is y = (5/2)x - 7, where the midpoint and slope of the perpendicular line are used in the calculation.

Step-by-step explanation:

To find the equation for the perpendicular bisector of the line segment with endpoints (9,1) and (-1,5), we need to follow these steps:

1. Calculate the midpoint of the line segment, which will be a point on the bisector. The midpoint (M) formula is M = ((x1 + x2) / 2, (y1 + y2) / 2).
2. Find the slope of the original line segment. The slope (m) formula is m = (y2 - y1) / (x2 - x1).
3. Determine the slope of the perpendicular bisector, which is the negative reciprocal of the slope of the original line.
4. Use the point-slope form of the equation y - y1 = m(x - x1), where (x1, y1) is the midpoint and m is the slope of the bisector.

Step-by-step calculation:

1. Midpoint M = ((9 - 1) / 2, (1 + 5) / 2) = (4, 3).
2. Slope of the line segment m = (5 - 1) / (-1 - 9) = 4 / -10 = -2/5. The slope of the perpendicular bisector is the negative reciprocal of -2/5, which is 5/2.
3. Using the point-slope form with M (4, 3) and slope 5/2, the equation is y - 3 = (5/2)(x - 4).

This simplifies to y = (5/2)x - 7, which is the equation of the perpendicular bisector.