Answer:
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Find the slope of the line passing through the given points:
- m = (3 - (-1)) / (-9 - 7)
- m = 4/ (-16)
- m = - 1/4
Perpendicular lines have negative- reciprocal slopes, so the perpendicular bisector has a slope of m = 4.
Find the midpoint of the segment with the endpoints (7, - 1) and (- 9,3).
- x = (7 - 9)/2 = -2/2 = - 1
- y = (-1 + 3)/2 = 2/2 = 1
Now, we need to find the line with a slope of 4 and passing through the point (- 1, 1). Use point-slope form and find the equation:
- y - 1 = 4(x - (-1))
- y - 1 = 4x + 4
- y = 4x + 5