Answer:
D. [tex](-21,16)[/tex]
Step-by-step explanation:
We have been that point, M, divides segment AB into a ratio of 4:7. Point A is at (-33,0) and B is at (0,44). We are asked to find the coordinates of point M.
We will use segment formula to solve our given problem.
When point P divides segment AB internally in the ratio m:n, then coordinates of point P can be found using formula:
[tex][{x=\frac{m\cdot x_2+n\cdot x_1}{m+n}, y=\frac{m\cdot y_2+n\cdot y_1}{m+n}][/tex]
Upon substituting our given values in above formula we will get,
[tex][{x=\frac{4\cdot 0+7\cdot -33}{4+7}, y=\frac{4\cdot 44+7\cdot 0}{4+7}][/tex]
[tex][{x=\frac{0+-231}{11}, y=\frac{176+0}{11}][/tex]
[tex][{x=\frac{-231}{11}, y=\frac{176}{11}][/tex]
[tex][{x=-21, y=16][/tex]
Therefore, the coordinates of point M are [tex](-21,16)[/tex] and option D is the correct choice.
