In the diagram on a lunar eclipse if the positions of sun,earth,moon are shown by(-4,6);(k,-2)and (5,-6) respectively ,find k value
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Step-by-step explanation:
Given In the diagram on a lunar eclipse if the positions of sun,earth,moon are shown by(-4,6);(k,-2)and (5,-6) respectively ,find k value
- Now the coordinates of position of sun, earth and moon in lunar eclipse.
- Therefore the points need to be collinear.
- The points x1 y1 x2 y2 and x3 y3 are collinear since the vertices is zero.
- So x1 (y2 – y3) + x2 (y3 – y1) + x3(y1 – y2) = 0
- So – 4(-2 – (- 6) + k (- 6 – 6) + 5 (6 – (- 2) = 0
- So – 4(4) – 12 k + 5(8) = 0
- So – 16 – 12 k + 40 = 0
- So 40 – 16 – 12 k = 0
- So 24 – 12 k = 0
- 24 = 12 k
- Or k = 24 / 12
- Or k = 2
- Therefore the value of k is 2
Reference link will be
https://brainly.in/question/3021031
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