point M on a segment with endpoints (-1, 1) and ( 7, 7) partitions the segment in a 3:5 ratio. Find M

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)

Agc and bgd are vertical angles