Question

In the diagram on lunar eclipse,if the position of sun , earth, moon are shown by (-4,6), (K,-2),(5,-6) respectively then find the value of k..
plz...It's urgent

Answer 1

If this is lunar eclipse so
They would be collinear
See attachment
Pls mark as brainliest if it will help you

Answer 2

Answer: The value of k is 2.

Explanation:

Here,  (-4,6), (k,2) and (5,-6) are the coordinates of the position of sun, earth and moon in lunar eclipse,

⇒ The points (-4,6), (k,2) and (5,-6) must be col linear.

Since, three points $(x_1,y_1)$, $(x_2,y_2)$ and $(x_3,y_3)$ are called col-linear if the area of the triangle, for which they are the vertices, is zero.

That is,

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

⇒ -4(-2-(-6)) + k(-6-6)+5(6-(-2)) = 0

⇒ -4(-2+6) + k(-12) + 5(6+2) = 0

⇒ -4(4) - 12k + 5(8) = 0

⇒ -16 - 12 k + 40 = 0

⇒ 24 - 12 k = 0

⇒ -12 k  = -24 ⇒ k = 2

Hence, the value of k is 2.