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
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