Question

If the points (K, -2), (-3, 8) and (-1,4) are collinear
find the value of k​

Answer 1

Given

Three points which are collinear

(k,-2) , (-3,8) , (-1,4)

To find :-

We have to find out the value of K

Solution :-

We know that formula of collinearity

$\sf\ \dfrac{1}{2}\big[x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)\big]=0\\ \\ \\ :\implies\sf\ x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)=0$

We have

$\bullet\sf\ \ x_1= k\ \ ;\ \bullet\ x_2=-3\ \ ;\ \bullet\ x_3=-1\\ \\ \bullet\sf\ y_1= -2\ \ ;\bullet\ y_2=8\ \ ; \bullet\ y_3= 4$

Now put the values in the given formula !

$:\implies\sf\ k(8-4)+(-3)\big\{4-(-2)\big\}+(-1)(-2-8)=0\\ \\ \\ \\ :\implies\sf\ 4k-(3\times 6)-(-10)=0\\ \\ \\ \\ :\implies\sf\ 4k-18+10=0\\ \\ \\ \\ :\implies\sf\ 4k-8=0\\ \\ \\ \\ :\implies\sf\ 4k=8\\ \\ \\ :\implies\sf\ k =\cancel{\dfrac{8}{4}}\\ \\ \\ \implies\underline{\boxed{\red{\mathsf k=2}}}$

Answer 2

Answer:

k = 2

Step-by-step explanation:

Formula:-

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

===> x1 =k ,x2 = -3,x3 = -1,

===>y1 =-2,y2 = 8,y3 = 4.

let's substitute all ,

==>K(8-4)+(-3){4-(-2)}+(-1)(-2-8)= 0

==>4k - (3×6) - (-10) = 0

==>4k-18 +10 = 0

==>4k-8 = 0

==>4k = 8

==>K = 8/4.

Hence, K = 2 is answer