Question

In the diagram on a lunner eclipe if the positions of sun earth and moon are shown by (-4 6) (k,-2) (5,-6) respectively the find the value of k​

Answer 1

ANSWER

As the sun, earth and moon lie on the same axis. Thus the points (−4,6),(k,−2) and (5,−6) are collinear.

As the sun, earth and moon lie on the same axis. Thus the points (−4,6),(k,−2) and (5,−6) are collinear.Therefore,

As the sun, earth and moon lie on the same axis. Thus the points (−4,6),(k,−2) and (5,−6) are collinear.Therefore,∣∣∣∣∣∣∣∣x1x2x3y1y2y3111∣∣∣∣∣∣∣∣=0

As the sun, earth and moon lie on the same axis. Thus the points (−4,6),(k,−2) and (5,−6) are collinear.Therefore,∣∣∣∣∣∣∣∣x1x2x3y1y2y3111∣∣∣∣∣∣∣∣=0∣∣∣∣∣∣∣∣−4k56−2−6111∣∣∣∣∣∣∣∣=0

As the sun, earth and moon lie on the same axis. Thus the points (−4,6),(k,−2) and (5,−6) are collinear.Therefore,∣∣∣∣∣∣∣∣x1x2x3y1y2y3111∣∣∣∣∣∣∣∣=0∣∣∣∣∣∣∣∣−4k56−2−6111∣∣∣∣∣∣∣∣=0−4(−2−(−6))−6(k−5)+1(−6k−(−10))=0

As the sun, earth and moon lie on the same axis. Thus the points (−4,6),(k,−2) and (5,−6) are collinear.Therefore,∣∣∣∣∣∣∣∣x1x2x3y1y2y3111∣∣∣∣∣∣∣∣=0∣∣∣∣∣∣∣∣−4k56−2−6111∣∣∣∣∣∣∣∣=0−4(−2−(−6))−6(k−5)+1(−6k−(−10))=0−16−6k+30−6k+10=0

As the sun, earth and moon lie on the same axis. Thus the points (−4,6),(k,−2) and (5,−6) are collinear.Therefore,∣∣∣∣∣∣∣∣x1x2x3y1y2y3111∣∣∣∣∣∣∣∣=0∣∣∣∣∣∣∣∣−4k56−2−6111∣∣∣∣∣∣∣∣=0−4(−2−(−6))−6(k−5)+1(−6k−(−10))=0−16−6k+30−6k+10=024−12k=0

As the sun, earth and moon lie on the same axis. Thus the points (−4,6),(k,−2) and (5,−6) are collinear.Therefore,∣∣∣∣∣∣∣∣x1x2x3y1y2y3111∣∣∣∣∣∣∣∣=0∣∣∣∣∣∣∣∣−4k56−2−6111∣∣∣∣∣∣∣∣=0−4(−2−(−6))−6(k−5)+1(−6k−(−10))=0−16−6k+30−6k+10=024−12k=0⇒k=1224