9514 1404 393
Answer:
y = -4/7x +58/7
Explanation:
The slope of the given line segment is ...
m = (y2 -y1)/(x2 -x1)
m = (17 -3)/(1 -(-7)) = 14/8 = 7/4
Then the slope of the perpendicular line is ...
-1/m = -4/7 . . . . . slope of the perpendicular bisector.
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The midpoint of the given line segment is ...
M = 1/2(x1 +x2, y1 +y2)
M = (1/2)(-7 +1, 3 +17) = 1/2(-6, 20) = (-3, 10)
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The y-intercept of the bisector can be found from ...
b = y -mx
b = 10 -(-4/7)(-3) = 10 -12/7 = 58/7
Then the slope-intercept form equation for the perpendicular bisector is ...
y = mx +b
y = -4/7x +58/7