A point M on a segment with endpoints X (1, −2) and Y (10, 3) partitions the segment in a 5:1 ratio. Find M. You must show all work to receive credit.

Answer 1

To obtain a 5:1 ratio, the x coordinate of M is 5/6 of the way between the x-coordinate of X (1) and the x-coordinate of Y (10).

5/6 of that distance = 5/6 * (10 - 1) = 7.5, which you add to the x-coordinate of X(1), to get the x-coordinate of M (8.5).

Similarly, the y-coordinate of M is 5/6 of the way between the y-coordinate of X (-2) and the y-coordinate of y (3). 5/6 of that distance = 5/6 * (3 - - 2) = 4.17, which you add to the y-coordinate of X(-2), to get the y-coordinate of M(2.17).

So the coordinates of M are (8.5,2.17)