Question

Evaluate x if the points (8.1) (x,-4) and (2,-5) are collinear​

Answer 1

Step-by-step explanation:

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Answer 2

Answer:

We know that for collinear points, the area of the triangle formed by them is 0.

Therefore, Area of triangle = 1/2(x1(y2-y3) + x2(y3-y1) + x3(y1-y2) = 0

Here x1 = 8, x2 = k,x3 = 2.

y1 = 1,y2 = -4,y3 = -5.

Hence,

1/2(8(-4-(-5) + k(-5-1) + 2(1 -(-4))) = 0

1(8(-4 + 5) + k(-6) + 2(1 + 4))= 0

8(1) + -6k + 2(5) = 0

8 - 6k + 10 = 0

-6k = -10-8

-6k = -18

k = 3.

Therefore the value of k = 3.