Question

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)

Answer 1

Given that M divides  segment AB in the ratio 4:7, to get the point M we proceed as follows:
A(-33,0); B(0,44)
4/11[(0--33),(44-0)]
=4/11(33,44)
=(12,16)
Thus the point will be:
M=[-33+12,16+0]
M=(-21,16)

Answer: D] (-21,16)

Answer 2

Answer:

D. $(-21,16)$

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:

$[{x=\frac{m\cdot x_2+n\cdot x_1}{m+n}, y=\frac{m\cdot y_2+n\cdot y_1}{m+n}]$

Upon substituting our given values in above formula we will get,

$[{x=\frac{4\cdot 0+7\cdot -33}{4+7}, y=\frac{4\cdot 44+7\cdot 0}{4+7}]$

$[{x=\frac{0+-231}{11}, y=\frac{176+0}{11}]$

$[{x=\frac{-231}{11}, y=\frac{176}{11}]$

$[{x=-21, y=16]$

Therefore, the coordinates of point M are $(-21,16)$ and option D is the correct choice.