Question

Given that Point A has coordinates (8,2) and Point B has coordinates (2,-10), find the coordinates of point P that partitions segment AB in a ratio of 5:1.

A)(6,-8)
B)(4,-6)
C)(7,0)
D)(5,-12)

Answer 1

To find the coordinates of point P that partitions segment AB in a ratio of 5:1, we use the section formula to calculate the coordinates.

Step-by-step explanation:

To find the coordinates of point P that partitions segment AB in a ratio of 5:1, we can use the section formula. The section formula states that the coordinates of a point P that divides a line segment AB in the ratio m:n is given by:

P = ((n * Ax) + (m * Bx)) / (m + n), ((n * Ay) + (m * By)) / (m + n)

Substituting the given values, we get:
P = ((1 * 8) + (5 * 2)) / (5 + 1), ((1 * 2) + (5 * -10)) / (5 + 1)

This simplifies to:
P = (18/6, -48/6)

Therefore, the coordinates of point P are (3, -8).This means that option B) (4,-6) is the correct answer.