Find the point, M, that divides segment AB into a ratio of 4:7 if A is at (-33,0) and B is at (0, 44).
(-22, 15)
(-22, 16)
(-21, 15)
(-21, 16)

(-21, 16)  

Step-by-step explanation:

A is at (-33, 0) and B is at (0, 44),

A point that divides the line segment in a ratio of 4:7 also divides the differences of the x-and y-coordinates in the same ratio.

If we divide each distance into 11 equal parts and choose a length 4/11  of the distance, the other part will be 7/11 of the distance. The two parts will be in a ratio of 4:7.

For the x-coordinate,

x₂ - x₁ = 0 - (-33) = 0 + 33 = 33

(4/11) × 33 = 12

-33 + 12 = -21

The x-coordinate of M is (-21, 0).

For the y-coordinate,

y₂ - y₁ = 44 - 0 = 44

(4/11) × 44 = 16

0 + 16 = 16

The y-coordinate of M is (0, 16).

The coordinates of M are then (-21, 16).

The diagram below shows the point M that divides AB in a 4/7 ratio.