find the value of k if the points A(2,6) B(4,k) and c(6,-2) are collinear.
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find the value of k if the points A(2,6) B(4,k) and c(6,-2) are collinear.
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Answer: K = 2
Step-by-step explanation:
Points are collinear
Therefore, Area of triangle is = 0
(The 3 points form a straight line, hence area = 0)
Using area of triangle formula,
A = (1/2) [x1 (y2- y3 )+x2 (y3-y1 )+x3(y1-y2)]
0 = 1/2* {2(k+2) + 4(-2-6) + 6(6-k)}
0 = {2(k+2) + 4(-8) + 6(6-k)}
0 = 2k + 4 -32 + 36 -6k
0 = -4k + 8
-8 = -4k
-8/-2 = k
2 = k
Hope this helps!!
Cheers!!