Respuesta :
Given:
Line segment AB has one endpoint at A(0,0).
(5, 3) is 1/3 of the way from A to B.
To find:
The coordinates of point B.
Solution:
Let the coordinates of point B are (a,b).
Suppose point P(5, 3) is 1/3 of the way from A to B.
[tex]\dfrac{AP}{AB}=\dfrac{1}{3}[/tex]
[tex]\dfrac{AP}{PB}=\dfrac{AP}{AB-AP}=\dfrac{1}{3-1}=\dfrac{1}{2}[/tex]
It means, point P(5, 3) divides the segment AB in 1:2.
Section formula:
If a point divides a line segment in m:n, then
[tex]Point=\left(\dfrac{mx_2+nx_1}{m+n},\dfrac{my_2+ny_1}{m+n}\right)[/tex]
Point P(5, 3) divides the segment AB in 1:2. Using section formula, we get
[tex]P=\left(\dfrac{1(a)+2(0)}{1+2},\dfrac{1(b)+2(0)}{1+2}\right)[/tex]
[tex](5, 3)=\left(\dfrac{a}{3},\dfrac{b}{3}\right)[/tex]
On comparing both sides, we get
[tex]\dfrac{a}{3}=5[/tex]
[tex]a=15[/tex]
[tex]\dfrac{b}{3}=3[/tex]
[tex]b=9[/tex]
Therefore, the coordinates of point B are (15,9).
Answer:
Line segment AB has one endpoint at A(0,0).
(5, 3) is 1/3 of the way from A to B.
Step-by-step explanation:
