Question

Find the perpendicular bisector in point-slope form of the line segment with endpoints (-2,6) and (4,-4).

Answer 1

To find the perpendicular bisector in point-slope form, calculate the midpoint, determine the negative reciprocal of the original slope, and apply the point-slope form equation with the slope of the bisector and the midpoint of the segment.

Step-by-step explanation:

The problem is to find the perpendicular bisector in point-slope form of the line segment with endpoints (-2,6) and (4,-4).

1. First, we need to find the midpoint of the segment to locate a point on the bisector. The midpoint formula is: ((x1 + x2)/2, (y1 + y2)/2). Using our points (-2,6) and (4,-4), the midpoint is ((-2 + 4)/2, (6 + (-4))/2) which simplifies to (1,1).
2. Next, we find the slope of the line segment using the formula (y2 - y1)/(x2 - x1). After substituting the values from our points, we get (-4 - 6)/(4 - (-2)) = -10/6. Simplified, the original slope is -5/3.
3. The slope of the perpendicular bisector will be the negative reciprocal of the original slope, so it will be 3/5.
4. Finally, we can use the point-slope form equation, y - y1 = m(x - x1), with our midpoint (1,1) and the slope of the bisector to get y - 1 = 3/5(x - 1).