Question

The endpoints of MN are located at M (-4,4) and N (2,-2). What are the coordinates of the point P that divides MN such that MP: PN is equal to 2: 1?

(-3.5, 2.5)
o
(-2,2)
(-1, 1)
(0,0)
Please help

Answer 1

The coordinates of point P that divides the segment MN in a 2:1 ratio are (0,0) found using the section formula for internal division of a line segment.

Step-by-step explanation:

The student asked for the coordinates of the point P that divides the segment MN into a ratio of 2:1, with points M (-4,4) and N (2,-2). To find the coordinates of point P, we can use the section formula for internal division. In this situation, we have the ratio as 2:1, which means m=2 and n=1. We apply the section formula (mx2 + nx1) / (m + n), (my2 + ny1) / (m + n) for the x and y coordinates respectively.

For the x-coordinate:
(2*2 + (-4)*1) / (2 + 1) = (4 - 4) / 3 = 0 / 3 = 0.
For the y-coordinate:
(2*(-2) + 4*1) / (2 + 1) = (-4 + 4) / 3 = 0 / 3 = 0.
Therefore, the coordinates of point P are (0,0).