Question

Suppose segment XY has one endpoint at X(0,0)

Answer 1

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

 $a=\frac{cq+ep}{p+q}$ and $b=\frac{dq+fp}{p+q}$

∵ 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

∵ $3=\frac{(0)(2)+e(1)}{1+2}$

∴ $3=\frac{0+e}{3}$

∴ $3=\frac{e}{3}$

- Multiply both sides by 3

∴ 9 = e

∴ The x-coordinate of point Y is 9

∵ $4=\frac{(0)(2)+f(1)}{1+2}$

∴ $4=\frac{0+f}{3}$

∴ $4=\frac{f}{3}$

- Multiply both sides by 3

∴ 12 = f

∴ The y-coordinate of point Y is 12

* The coordinates of point Y are (9 , 12)