Question

In the diagram on a lunar eclipse , if the positions of sun , earth and moon shown by (-4,6),(K,-2)and (5,-6) respectively, then find the value of K​

Answer 1

We know that lunar eclipse occurs when the sun, earth and moon are very closely situated as in a straight line with earth between the sun and the moon. So that the sun, earth and moon are on a straight line here.

Thus the positions (-4, 6), (k, -2) and (5, -6) are collinear. Hence the slope with any two points among them remain same.

With (-4, 6) and (k, -2), slope is,

m = (- 2 - 6) / (k - (-4))

m = - 8 / (k + 4) → (1)

With (k, -2) and (5, -6), slope is,

m = (- 2 - (-6)) / (k - 5)

m = 4 / (k - 5) → (2)

From (1) and (2),

- 8 / (k + 4) = 4 / (k - 5)

- 8 (k - 5) = 4 (k + 4)

- 8k + 40 = 4k + 16

12k = 24

k = 2

Hence 2 is the answer.

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