Question

Given the points A(5,-1) and B(-5,3), find the coordinates of the point P on the directed line segment AB that partitions AB in the ratio 1:3.

Answer 1

To find the coordinates of the point P that partitions AB in the ratio 1:3, we can use the section formula. Using the given coordinates of A(5,-1) and B(-5,3), the coordinates of P are (2.5, 0).

Step-by-step explanation:

To find the coordinates of the point P that partitions AB in the ratio 1:3, we can use the section formula. In this formula, the x-coordinate of P is found by taking (3/4) times the x-coordinate of A plus (1/4) times the x-coordinate of B. Similarly, the y-coordinate of P is found by taking (3/4) times the y-coordinate of A plus (1/4) times the y-coordinate of B.

Using the given coordinates of A(5,-1) and B(-5,3), we can substitute these values into the section formula and solve for the coordinates of P.

Let's plug the values into the formula:
x-coordinate of P = (3/4) * 5 + (1/4) * -5 = 15/4 + -5/4 = 10/4 = 2.5
y-coordinate of P = (3/4) * -1 + (1/4) * 3 = -3/4 + 3/4 = 0
Therefore, the coordinates of point P are (2.5, 0).