A line contains points (2, -2) and (-4, 1). Another line graphed in the same coordinate plane contains points (1, 2) and (-3, 4). Based on the slopes of these lines, are they parallel, perpendicular or neither?

Question

anonymous · Answer

Find the slope.
$$Slope = \frac{ y2 - y2 }{ x2 - x1}$$

(2, -2) and (-4, 1):
$$slope = \frac{ 1 -(-2) }{(-4) - 2  } = \frac{ 1 + 2 }{(-4) - 2 } = \frac{ 3 }{ -6 } =-\frac{ 1 }{ 2 } $$Slope is -1/2


 (1, 2) and (-3, 4):
$$slope = \frac{ 4 - 2 }{ (-3) - 1 } = \frac{ 2 }{ -4 } = -\frac{1 }{ 2 }$$Slope is -1/2


------------------------
Parallel lines have the same slope
Slope of Perpendicular lines is opposite-reciprocal.

anonymous · Answer

So, based on the slopes of these lines, are they parallel, perpendicular or neither?