Answer:
(–1, 1) and (–6, –1)
(1, 0) and (6, 2)
(3, 0) and (8, 2)
Step-by-step explanation:
Slope of line having points (x1, y1) and (x2,y2) is given by (y2-y1)/(x2-x1)
Two lines with slope m1 and m2 are parallel if there slopes are equal i.e m1 = m2.
Slope of line that contains (3, 4) and (–2, 2)
m = (2-4)/(-2-3) = -2/-5 = 2/5
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To find if other pair of lines lie on line parallel to line that contains (3, 4) and (–2, 2), we need to find slope for other pair of points , if those pairs have slopes as 2/5 then its clear that they lie on line parallel to line that contains (3, 4) and (–2, 2) else not.
Lets find slope of all the pairs
(–2, –5) and (–7, –3)
m1 = -3 -(-5)/-7-(-2) = -3+5/-7+2
m1 = 2/-5 = -2/5
as -2/5 is not equal to 2/5, the mentioned points do not lie on line parallel to line that contains (3, 4) and (–2, 2).
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(–1, 1) and (–6, –1)
m2 = -1 -1)/-6-(-1) = -2/-6+1
m2 = -2/-5 = 2/5
as 2/5 is equal to 2/5, the mentioned points do lie on line parallel to line that contains (3, 4) and (–2, 2).
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(0, 0) and (2, 5)
m3 = 5 -0)/2-0
m3 = 5/2
as 5/2 is not equal to 2/5, the mentioned points do not lie on line parallel to line that contains (3, 4) and (–2, 2).
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(1, 0) and (6, 2)
m4 = 2 -0)/6-1
m4 = 2/5
as m4
As m4 is equal to 2/5, the mentioned points do lie on line parallel to line that contains (3, 4) and (–2, 2).
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(3, 0) and (8, 2)
m5 = 2 -0)/8-3
m5 = 2/5
as m5 is equal to 2/5, the mentioned points do lie on line parallel to line that contains (3, 4) and (–2, 2).
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Thus, pair of points which lie on lie on line parallel to line that contains (3, 4) and (–2, 2) are
(–1, 1) and (–6, –1)
(1, 0) and (6, 2)
(3, 0) and (8, 2)
