Question

In the diagram on a lunar eclipse if the positions of sun Earth and Moon are shown by (-4,6) (k, -2) (5,-6) respectively then find the value of k

Answer 1

For lunar eclipse to happen they have to be in a straight line .It means that the centres must lie in a straight line .One of the characteristics by which we can understand the line is from it's slope .
So

slope = {(6--2)/(-4-k)} = {(-6+2)/(5-k)}


On cross multiplying and solving for k
2(5-k)=k+4
k=2