Answer:
The coordinates of point Y are (9 , 12)
Step-by-step explanation:
* Lets explain how to solve the problem
- If point (a , b) divides a line whose end points are (c , d) and (e , f) at
ratio p : q from the point (c , d), then
[tex]a=\frac{cq+ep}{p+q}[/tex] and [tex]b=\frac{dq+fp}{p+q}[/tex]
∵ Segment XY has one endpoint at X (0 , 0)
∵ Point (3 , 4) is 1/3 of the way from X to Y
∴ Point (3 , 4) divides the segment XY, where the distance from X
to the point (3 , 4) is 1 part and from point (3 , 4) to Y is 2 parts
∴ Point (3 , 4) divides segment XY to the ratio 1 : 2 from X
- Let point (a , b) is (3 , 4)
- Let point (c , d) is X (0 , 0)
- Let point (e , f) is Y
- Let p : q = 1 : 2
* Lets find e and f
∵ [tex]3=\frac{(0)(2)+e(1)}{1+2}[/tex]
∴ [tex]3=\frac{0+e}{3}[/tex]
∴ [tex]3=\frac{e}{3}[/tex]
- Multiply both sides by 3
∴ 9 = e
∴ The x-coordinate of point Y is 9
∵ [tex]4=\frac{(0)(2)+f(1)}{1+2}[/tex]
∴ [tex]4=\frac{0+f}{3}[/tex]
∴ [tex]4=\frac{f}{3}[/tex]
- Multiply both sides by 3
∴ 12 = f
∴ The y-coordinate of point Y is 12
* The coordinates of point Y are (9 , 12)