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Question 390297: Hi,
I need help on the following questions and please explain how you did them.
1) show that (4,4) is one the perpendicular bisector of the line segment joining (-2,12) and (4,-6).
2) find the value of K for which the line joining (2.1,3.3) and (K,-3.2) is parallel to the line joining (-1,-2) and (1,3).
Thank you so much!!!
Answer by ewatrrr(24785)   (Show Source):
You can put this solution on YOUR website!
Hi
Midpoint (  ,  )
Midpoint for line segment joining(-2,12) and (4,-6).
Midpoint is Pt(1, 3) slope of that segment is -6-12 / 4-(-2) = -18/6 = -3
slope of segment joining (4,4) and (1,3) is 3-4 /1-4 = -1/-3 = 1/3
slopes of two segments are negative reciprocals of one another,
thus segments ⊥ to one another.
2) find the value of K for which the line joining (2.1,3.3) and (K,-3.2) is parallel to the line joining (-1,-2) and (1,3).
parallel lines have identical slopes
line joining (-1,-2) and (1,3) has slope: 3-(-2) / 1-(-1) = 5/2
line joining (2.1,3.3) and (K,-3.2): -3.2 - 3.3 / K - 2.1 = -6.5/(K - 2.1)
-6.5/(K - 2.1) = 5/2
5(K-2.1) = -2*6.5
5K - 10.5 = -13
5K = -2.5
K = -.5
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