Answer: Yes, they are perpendicular
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Work Shown:
Find the slope of line A
m = (y2-y1)/(x2-x1)
m = (2-(-2))/(5-(-3))
m = (2+2)/(5+3)
m = 4/8
m = 1/2
The slope of line A is 1/2.
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Repeat for the slope of line B
m = (y2-y1)/(x2-x1)
m = (2-(-6))/(-1-3)
m = (2+6)/(-1-3)
m = 8/(-4)
m = -2
The slope of line B is -2
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Since the second slope is the negative reciprocal of the first slope, this means the two lines are perpendicular.
Put another way: the two slopes (-2 and 1/2) multiply to -1, so the lines are perpendicular.