Question

Find the coordinates of p so the p partitions AB in the ratio 3:2 if A.(1,5) and B. (6,10)​

Answer 1

The coordinates of point P, which divides the line segment AB in the ratio of 3:2 with A being (1,5) and B being (6,10), are found using the section formula. The resulting coordinates of P are (4, 8).

Step-by-step explanation:

The question is asking to find the coordinates of point P that divides the line segment AB in the ratio of 3:2, where A is (1,5) and B is (6,10). To find the coordinates of point P, we use the section formula, which is used in coordinate geometry to find a point that divides a line segment into a given ratio.

Here’s how to apply the section formula:

1. For the x-coordinate: Px = [(m × Bx) + (n × Ax)] / (m + n)
2. For the y-coordinate: Py = [(m × By) + (n × Ay)] / (m + n)

In this example, we substitute A(1,5), B(6,10), and the ratio m:n = 3:2 into the formula.

The calculations are:

• x-coordinate of P: Px = (3×6 + 2×1)/(3 + 2) = (18 + 2)/5 = 20/5 = 4
• y-coordinate of P: Py = (3×10 + 2×5)/(3 + 2) = (30 + 10)/5 = 40/5 = 8

Therefore, the coordinates of point P are (4, 8).