Question

mlis toWhat are the coordinates of the point on the directed line segmentfrom (-6, -5) to (9, 1) that partitions the segment into a ratio of 2to 1?ingill b

Answer 1

Let P represent the point and xp and yp represent the coordinates of the point, P.

If P(xp, yp) divides a line segment from A(x1, y1) to B(x2,y2) in the ratio, a:b, then

xp = x1 + a(x2 - x1)/(a + b)

yp = y1 + a(y2 - y1)/(a + b)

From the information given,

x1 = - 6, y1 = - 5

x2 = 9, y2 = 1

a = 2, b = 1

xp = - 6 + 2(9 - - 6)/(2 + 1)

xp = - 6 + 30/3

xp = - 6 + 10

xp = 4

yp = - 5 + 2(1 - - 5)/(2 + 1)

yp = - 5 + 12/3

yp = - 5 + 4

yp = - 1

The coordinates of the point is (4, - 1)