Find the value of 'K' for which the points are collinear (8,1),(K,-4),(2,-5).
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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.
Hope this helps!
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.
Hope this helps!
but I want to know that..
What?
if points are collinear the why area of triangle is 0
Let me tell you in a more simple way.If they are collinear, they will lie on the same line. Then they won't form a triangle.
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