Q. 194.6( 7 Votes )

# Find the value of k, if the points A (8, 1), B (3, - 4) and C (2, k) are collinear.

Answer :

Given points are *A*(8*,*1)*,B*(3*,−*4) and *C*(2*,k*).It is also said that they are collinear and hence the area enclosed by them should be 0.

Area of the triangle having vertices (x_{1},y_{1}), (x_{2},y_{2}) and (x_{3},y_{3})

= |x_{1}(y_{2}-y_{3})+x_{2}(y_{3}-y_{1})+x_{3}(y_{1}-y_{2})|

Given that area of ∆ABC = 0

∴ 0 = |8(-4 – k) + 3(k – 1) + 2(1 – (-4))|

∴ 0 = |-32 – 8k + 3k -3 + 10|

∴ 5k + 25 = 0

∴ k = -5

Hence, the value of k is -5.

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