Math, asked by dishayadav8521, 1 month ago

In each of the following find the value of k, for which the points are collinear.
(i) (7,−2),(5,1),(3,k)
(ii) (8,1),(k,−4),(2,−5)

Answers

Answered by shubhamsinha3013
0

Answer:

Concept:

Collinear derived from 2 word co and linear co means together and linear means on the line

So, collinear point are point that all lie in the same line.

Find:

We have find the value of k

Given:

We given that the points

(i) (7,-2),(5,1),(3,k)

(ii) (8,1),(k,-4),(2,-5)

are collinear

Step-by-step explanation:

We know that point are collinear means area of triangle is O

Area of triangle = 0

1/2(x1(y2-y3)+x2(y3-y1)+x3(y1-y2)=0

(i) (7,-2),(5,1),(3,k)

Area of triangle = 0

1/2(x1(y2-y3)+x2(y3-y1)+x3(y1-y2)=0

1/2(7(1-k)+5(k-(-2)) +3(-2-(-1))=0

1/2(7-7k+5k+10-3) =0

1/2(-2k+14)=0

-2k+14=0

-2k=-14

k=14/2

k=7

Hence the value of k is 7

ii) (8,1),(k,-4),(2,-5)

Area of triangle = 0

1/2(x1(y2-y3)+x2(y3-y1)+x3(y1-y2)=0

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

1/2(8-6k+10) =0

1/2(-6k+18)=0

-6k+18=0

-6k=-18

k=18/6

k=3

Hence the value of k is 3

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