Question

in the diagram on a Lunar eclipse if the position of Sun , Earth and moon are shown by (-4,6) (k,-2) (5,-6) respectively then find value of k

Answer 1

Since it is an eclipse, the three points are collinear (the three points lie on the same straight line)

Therefore,

n1(y2 –y3) + n2(y3-y1) +n2(y1-y2) = 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 – 12k + 40 = 0

24 = 12k

k = 2

Answer