Answer:
Step-by-step explanation:
The coordinates of the point that partitions the line segment from (-2, -2) to (9, 9) into a ratio of 5 to 6 is the point (5.5, 5.5).
To find the coordinates of this point, we need to use the formula for the midpoint of a line segment:
Midpoint = (x1 + x2)/2, (y1 + y2)/2
In this case, x1 = -2, x2 = 9, y1 = -2, y2 = 9.
Therefore, the midpoint = (-2 + 9)/2, (-2 + 9)/2
Substituting the values:
Midpoint = (7/2, 7/2)
Since the midpoint has to be in the ratio of 5 to 6, we divide each of the components of the midpoint by 11/6:
Midpoint = (7/2)/(11/6), (7/2)/(11/6)
Simplifying:
Midpoint = (15/22, 15/22)
Therefore, the coordinates of the point that partitions the line segment from (-2, -2) to (9, 9) into a ratio of 5 to 6 is the point (5.5, 5.5).