Question

Point A has coordinates (2, 4). Point B has coordinates

(10,12). Find the coordinates of point P that partitions AB
In the ratio 3:2.

Answer 1

The coordinates of point P that partitions the line segment AB in the ratio 3:2 are (6.8, 8.8), found using the section formula.

Step-by-step explanation:

To find the coordinates of a point P that partitions the line segment AB in the ratio 3:2, we can use the section formula. The section formula for a point P dividing the line segment AB in the ratio m:n (where P is closer to A) is given by:

Coordinates of P = [ (mx2 + nx1) / (m + n), (my2 + ny1) / (m + n) ]

Where A has coordinates (x1, y1) and B has coordinates (x2, y2).

Given A(2, 4) and B(10, 12), and using the ratio m:n = 3:2, we have:

Coordinates of P = [ (3×10 + 2×2) / (3 + 2), (3×12 + 2×4) / (3 + 2) ]

Coordinates of P = [ (30 + 4) / 5, (36 + 8) / 5 ]

Coordinates of P = [ 34 / 5, 44 / 5 ]

Coordinates of P = (6.8, 8.8)

Therefore, the coordinates of point P that partitions the line segment AB in the ratio 3:2 are (6.8, 8.8).