Question

Given the points A(-1, 2) and B(7, 10), find the coordinates of the point P on the directed line segment AB that partitions AB in the ratio 1:3 from A to B. Enter your answer as an ordered pair (x, y). Do not include any spaces in your ordered pair.

Answer 1

To find the coordinates of the point P that partitions the line segment AB in the ratio 1:3 from A to B, we can use the section formula. Using the given points A(-1, 2) and B(7, 10), we can substitute the values into the section formula to find the coordinates of point P as (2/3, 5/3).

Step-by-step explanation:

To find the coordinates of the point P that partitions the line segment AB in the ratio 1:3 from point A to point B, we can use the concept of section formula. The section formula states that if we have two points A(x1, y1) and B(x2, y2) and we want to find the coordinates of a point P on the line segment AB that divides it in a given ratio, we can use the formula:

x = (x1 + (m * x2)) / (1 + m)

y = (y1 + (m * y2)) / (1 + m)

Here, m represents the ratio.

For this question, let's substitute the given values:

Coordinates of A: x1 = -1, y1 = 2

Coordinates of B: x2 = 7, y2 = 10

Ratio: 1:3

Let's calculate the coordinates of P:

x = (-1 + (1/3 * 7)) / (1 + 1/3) = (2/3)

y = (2 + (1/3 * 10)) / (1 + 1/3) = (5/3)

Therefore, the coordinates of the point P are (2/3, 5/3).