Find the coordinates of point Q that lies along the directed line segment from R(-2, 4) to S(18, -6) and partitions the segment in the ratio of 3:7.

Question

1. A. (4, 1)
2.  B. (8, -1)
3.  C. (16, -2)
4.  D. (6, -3)

Answer 1

By Internal section formula ,

the coordinate of M is

Q={[(mx2+nx1)/(m+n)],[(my2+ny1)/(m+n)]}

Given

m: n = 3:7

Given that,

R(-2,4)=(x1,y1),

S(18,-6)=(x2,y2)

now you can find the co ordinate of Q by substituting all values

Q = {[3(18)+7(-2)/ 3+7 ],[(3(-6) +7(4))/ 3+7 ]}

={[ 54-14 / 10 ],[-18+28 / 10]}

={40/10 ,10/10 }

=(4,1)

so answer is A

Answer 2

The length of the line is sqrt{ (-6-4)² + (18+2)² } = 22.36

A ratio of 3:7 would mean that the answer point would partition the line into 3/10 & 7/10 of the line.

If you look at each answer:

A) (4,1) , the length from (-2,4) to this point is 6.7

6.7/22.36 = .3

B) (8,-1), the length from (-2,4) to this point is 11.18

11.18/22.36 = .5

C) (16,-2), the length from (-2,4) to this point is 18.97.

18.97/22.36 = .85

D) (6,-3), the length from (-2,4) to this point is 10.63

10.63/22.63 = .47

Therefore, the only point that has a 3/10 or 7/10 ratio is A !