Let P represent the point and xp and yp represent the coordinates of the point, P.
If P(xp, yp) divides a line segment from A(x1, y1) to B(x2,y2) in the ratio, a:b, then
xp = x1 + a(x2 - x1)/(a + b)
yp = y1 + a(y2 - y1)/(a + b)
From the information given,
x1 = - 6, y1 = - 5
x2 = 9, y2 = 1
a = 2, b = 1
xp = - 6 + 2(9 - - 6)/(2 + 1)
xp = - 6 + 30/3
xp = - 6 + 10
xp = 4
yp = - 5 + 2(1 - - 5)/(2 + 1)
yp = - 5 + 12/3
yp = - 5 + 4
yp = - 1
The coordinates of the point is (4, - 1)
