Question

Find the point Q along the directed line segement from point R (-3, 3) to point S(6, -3) that divides the segment in the ratio 2:1.

A. (3, 0)
B. (6, -4)
C. (0, 1)
D. (3, -1)

Answer 1

D

Explanation:

using the section formula

(x₁, y₁ ) and (x₂, y₂ ) divided in the ratio m : n , then

point = (
`(mx_(2)+nx_(1) )/(m+n)` ,
`(my_(2)+ny_(1) )/(m+n)` )

thus for R (- 3, 3 ) and S (6, - 3 ) in the ratio 2 : 1

Q = (
`(2(6)+1(-3))/(2+1)` ,
`(2(-3)+1(3))/(2+1)` )

= (
`(12-3)/(3)` ,
`(-6+3)/(3)` )

= (
`(9)/(3)` ,
`(-3)/(3)` )

= (3, - 1 )

Answer 2

Answer: (3,-1)

Explanation:

distance between R & S x values: 9

distance between R & S y values: -6

multiply each by 2/3 (the proportion)

9/1 x 2/3 = 6; -6/1 x 2/3= -4

add the answers to R x & y values:

-3 + 6= 3; 3 - 4= -1