Question

The coordinates of the endpoints of MN are M(-7,-6) and N(1,2). Point O is on MN and divides it such that MO:NO is 3:1. Are the coordinates of O?

a) (-4, -4)
b) (-2, -3)
c) (0, -2)
d) (2, -1)

Answer 1

To find the coordinates of point O, we need to determine the coordinates that divide the line segment MN in a 3:1 ratio. The coordinates of point O are (17, 18).

Step-by-step explanation:

To find the coordinates of point O, we need to determine the coordinates that divide the line segment MN in a 3:1 ratio.

First, we find the differences in the x-coordinates and y-coordinates between the endpoints: Δx = 1 - (-7) = 8 and Δy = 2 - (-6) = 8.

Next, we multiply Δx and Δy by the ratio 3:1 to find the distances from point M to point O: 3(Δx) = 3(8) = 24 and 3(Δy) = 3(8) = 24.

Finally, we add the distances to the coordinates of point M to find the coordinates of point O: x-coordinate = -7 + 24 = 17 and y-coordinate = -6 + 24 = 18. Therefore, the coordinates of point O are (17, 18). Since none of the answer choices match, none of them are correct.