SOLUTION: Find the value of a if b(3,4) c(a, 6) and d(a+5, 23) are collinear, explain.

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Question 1036379: Find the value of a if b(3,4) c(a, 6) and d(a+5, 23) are collinear, explain.
Answer by Alan3354(69443) About Me  (Show Source):
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Find the value of a if b(3,4) c(a, 6) and d(a+5, 23) are collinear
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If they're colinear the slopes have to be equal.
slope, m = diffy/diffx
m1 of bc = (6-4)/(a-3) = 2/(a-3)
m2 of bd = (23-4)/(a+5 - 3) = 19/(a+2)
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m1 = m2
2/(a-3) = 19/(a+2)
Cross multiply
2(a+2) = 19(a-3)
2a+4 = 19a-57
17a = 61
a = 61/17