Question 1202748: which of the following best describes the relationship between the two given coplanar segments?
segment pq: p(5, 2) q(-1, 6)
segment ab: a(-2, 3) b(4, -1)
a. parallel
b. perpendicular
c. neither
d. skew
Found 2 solutions by josgarithmetic, math_tutor2020:
Answer by josgarithmetic(39630)   (Show Source):
You can put this solution on YOUR website! Find the slope for the two pair of points. The answer will become apparent very fast.
PARALLEL.
(You find the steps necessary.)
Answer by math_tutor2020(3817) (Show Source):
You can put this solution on YOUR website!
Answer: Parallel
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Work Shown:
Slope of PQ
P = (x1,y1) = (5,2) and Q = (x2,y2) = (-1,6)
m = slope = rise/run = (change in y)/(change in x)
m = (y2 - y1)/(x2 - x1)
m = (6 - 2)/(-1 - 5)
m = (4)/(-6)
m = -2/3
The slope of line PQ is -2/3.
Slope of AB
A = (x1,y1) = (-2,3) and B = (x2,y2) = (4,-1)
m = slope = rise/run = (change in y)/(change in x)
m = (y2 - y1)/(x2 - x1)
m = (-1 - 3)/(4 - (-2))
m = (-1 - 3)/(4 + 2)
m = (-4)/(6)
m = -2/3
Line AB also has a slope of -2/3
A slope of -2/3 means "go down 2, go right 3".
slope = rise/run = -2/3
rise = -2 = go down 2
run = 3 = go right 3
Both lines have a slope of -2/3, so the lines are either parallel or the lines overlap entirely.
Use the point-slope template
to determine the equation of each line.
I'll let the student do this part.
You should find the y intercepts are different.
Parallel lines have equal slopes but different y intercepts.
I recommend GeoGebra and Desmos as two graphing options.
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