Question

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

Answer 1

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