Final answer:
The equation for the perpendicular bisector of the line segment with endpoints (-8, -2) and (4, 6) is y = (-3/2)x + 5.
Step-by-step explanation:
To find an equation for the perpendicular bisector of the line segment with endpoints (-8, -2) and (4, 6), follow these steps:
- Calculate the midpoint of the line segment, which will be a point on the bisector.
- Determine the slope of the line segment, then find the negative reciprocal to get the slope of the perpendicular bisector.
- Use the point-slope form to write the equation of the bisector.
Step 1: The midpoint (M) is calculated as M = ((-8 + 4)/2, (-2 + 6)/2) which simplifies to M = (-2, 2).
Step 2: The slope (m) of the line segment is (6 - (-2))/(4 - (-8)) = 8/12 = 2/3. The slope of the perpendicular bisector is the negative reciprocal of 2/3, which is -3/2.
Step 3: Using the point-slope form y - y1 = m(x - x1), with M = (-2, 2) and m = -3/2, we get y - 2 = (-3/2)(x - (-2)), which simplifies to the perpendicular bisector equation y = (-3/2)x + 5.