Question

A line segment begins at the point (-4,-9) and ends at the point (21, 31.625).

What are the coordinates of the point that partitions this line segment into two line segments whose lengths are in the ration of 2:3?

Answer 1

(6 , 7.25)

Explanation:

Given in the question coordinates (-4,-9) and (21,31.625)

x1 = -4

y1 = -9

x2 = 21

y2 = 31.625

Ratio

a : b

2 : 3

Formula to use

x = x1 +
`(a)/(a+b)`(x2-x1)

y = y1 +
`(a)/(a+b)`(y2 -y1)

Plug values on the formula

x = -4 +
`(2)/(2+3)(21+4)`

x = 6

y = -9 +
`(2)/(2+3)(31.625+9)`

y = 7.25

Co-ordinates of the point which divide the line into 2:3 is

(6 , 7.25)