Determine whether the line through the first pair of points is parallel to, perpendicular to, or neither parallel nor perpendicular to the line through the second pair of points.
a. (1,3) and (-1,-1)
(2,1) and (3,3)
b. (3,1) and (6,3)
(2,-1) and (4,-4)
c. (1,7) and (-1,-1)
(1,1) and (-1,9)
Answers & Comments
Determine whether the line through the first pair of points is parallel to, perpendicular to, or neither parallel nor perpendicular to the line through the second pair of points.
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Solution : Let
be the slope of the line through
and
and
be the slope of the line through
and
Then
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Solution :
Line through
and
slope
Line through
and
slope ![\sf {m_{2} = \frac{ - 4 - ( - 1)}{4 - 2} = \frac{ - 3}{3}} \\ \sf {m_{2} = \frac{ - 4 - ( - 1)}{4 - 2} = \frac{ - 3}{3}} \\](https://tex.z-dn.net/?f=%20%5Csf%20%7Bm_%7B2%7D%20%3D%20%20%5Cfrac%7B%20-%204%20-%20%28%20-%201%29%7D%7B4%20-%202%7D%20%20%3D%20%20%5Cfrac%7B%20-%203%7D%7B3%7D%7D%20%5C%5C%20)
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Solution :
Line through
and
slope ![\sf {m_{1} = \frac{ - 1 - 7}{ - 1 - 1} = \frac{ - 8}{ - 2} = 4} \\ \sf {m_{1} = \frac{ - 1 - 7}{ - 1 - 1} = \frac{ - 8}{ - 2} = 4} \\](https://tex.z-dn.net/?f=%20%5Csf%20%7Bm_%7B1%7D%20%3D%20%20%5Cfrac%7B%20-%201%20-%207%7D%7B%20-%201%20-%201%7D%20%20%3D%20%20%5Cfrac%7B%20-%208%7D%7B%20-%202%7D%20%20%3D%204%7D%20%5C%5C%20)
Line through
and
slope ![\sf {m_{2} = \frac{9 - 1}{ - 1 - 1} = \frac{8}{ - 2} = \: - 4} \\ \sf {m_{2} = \frac{9 - 1}{ - 1 - 1} = \frac{8}{ - 2} = \: - 4} \\](https://tex.z-dn.net/?f=%20%5Csf%20%7Bm_%7B2%7D%20%3D%20%20%5Cfrac%7B9%20-%201%7D%7B%20-%201%20-%201%7D%20%20%3D%20%20%5Cfrac%7B8%7D%7B%20-%202%7D%20%20%3D%20%5C%3A%20%20%20-%204%7D%20%5C%5C%20)
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