Q15 of 184 Page 10

In what ratio does the point (-4,6) divide the line segment joining the point A(-6,10) and B (3,-8)?

Let C(-4, 6) divides the line segment AB in the ratio m:n



Here, (x, y) = (-4, 6); (x1, y1) = (-6, 10) and (x2, y2) = (3, -8)


So,


⇒ -4m -4n = 3m - 6n and 6m + 6n = -8m + 10n


⇒ -4m – 3m – 4n + 6n = 0 and 6m + 8m + 6n – 10n = 0


⇒ -7m + 2n = 0 and 14m - 4n = 0


⇒ -7m = -2n and 14m = 4n


⇒ 7m = 2n and 7m = 2n



Hence, the ratio is 2:7 and the division is internal.


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