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(2,-1)(-3,5)1:2find the point that partitions the segment with the two given endpoints with the given ratio

User Egor Chiglintsev
by
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1 Answer

13 votes
13 votes

We are given two points

A = (2, -1)

B = (-3, 5)

Ratio = 1:2

Let the ratio be P

Therefore, P is 1:2

Slope = Rise / Run

Rise = y2 - y1

Run = x2 - x1

x1 = 2, y1 = -1, x2 = -3 and y2 = 5

P = 1 / 1+ 3

P = 1/3

The horizontal distance is the same as run

Run = x2 - x1

=-3 - 2

Run = -5

Therefore we have

P x run

1/3 x -5

= -5/3

The distance between P and A on the x - axis is

-5/3 - 2

= -11/3

Rise = y2 - y1

5 - (-1)

= 5 + 1

Rise = 6

1/3 x 6

6/3 = 2

The distance between A and P on the y axis is

2 -(-1)

=2 + 1

= 3

The points are -11/3 and 3

The answer is (-11/3, 3)