Q15 of 184 Page 10

Find the ratio in which (-8,3) divides the line segment joining the points (2,-2) and (-4,1).

Let C(-8, 3) divides the line segment AB in the ratio m:n



Here, (x, y) = (-8, 3); (x1, y1) = (2, -2) and (x2, y2) = (-4,1)


So,


⇒ -8m -8n = -4m + 2n and 3m + 3n = m - 2n


⇒ -8m + 4m - 8n - 2n = 0 and 3m – m + 3n + 2n = 0


⇒ -4m – 10n = 0 and 2m + 5n = 0


⇒ -2m – 5n = 0 and 2m + 5n = 0


⇒ 2m + 5n = 0 and 2m + 5n = 0


⇒ 2m = -5n



Hence, the ratio is 5:2 and this negative sign shows that the division is external.


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