Question

find the value of k if the points (k,-1) (2,1) (4,5) are collinear. Use area of triangle formula​

Answer 1

Answer:

Step-by-step explanation:

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

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

K*-4+12-8=0

-4K+4=0

-4K=-4

K=-4/-4

K=1 answer

Answer 2

The value of k is 1.

Given:

The points (k,-1), (2,1), and (4,5) are collinear

To find :

The value of k.

Solution :

Consider the given points.

(k,−1),(2,1) and (4,5)

Since these points are collinear means that the area of a triangle must be zero.

So,

$1/2 ( x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2))=0$

Therefore,

$k(1-5)+2(5+1)+4(-1-1)=0$

$k(-4)+2(6)+4(-2)=0$

$-4k+12-8=0$

$-4k+4=0$

$4k=4$

$k=1$

Therefore, the value of k is 1.

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