Question

The endpoints of AB are A(1, 4) and B(5, -1). What are the coordinates of the point that divides AB in the ratio 2 : 3

Answer 1

the answer is (2.6, 2)

Answer 2

First, we have to find the distance between the points A and B.
But there is a problem with the point B. It should be (5, 1)
Using distance formula,

d = √(x₂ - x₁)² + (y₂ - y₁)²

d = √(5-1)² + (1-4)²

d = √(4)² + (-3)²

d = √16 + 9

d = √25

d = 5

Now,
we will divide 5 by the total ratio, that is, 3 + 2 = 5
and
5 ÷ 5 = 1
The larger portion of the line AB will be: 1 × 3 = 3
The smaller portion of the line AB will be: 1 × 2 = 2
Let,
3 is the distance from A to C
and
2 is the distance from C to B.

You can find the points if the angle was given to you using the formula:

x₂ = x₁ × d × cosФ
y₂ = y₁ × d × sinФ

Some information in the question is missing, there was suppose to be an angle.