Question

Suppose line segment AB has one endpoint at A(0, 0). What are the coordinates of B if (5, 3) is 1/3 of the way from A to B?

Answer 1

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.

$\dfrac{AP}{AB}=\dfrac{1}{3}$

$\dfrac{AP}{PB}=\dfrac{AP}{AB-AP}=\dfrac{1}{3-1}=\dfrac{1}{2}$

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

$Point=\left(\dfrac{mx_2+nx_1}{m+n},\dfrac{my_2+ny_1}{m+n}\right)$

Point P(5, 3) divides the segment AB in 1:2. Using section formula, we get

$P=\left(\dfrac{1(a)+2(0)}{1+2},\dfrac{1(b)+2(0)}{1+2}\right)$

$(5, 3)=\left(\dfrac{a}{3},\dfrac{b}{3}\right)$

On comparing both sides, we get

$\dfrac{a}{3}=5$

$a=15$

$\dfrac{b}{3}=3$

$b=9$

Therefore, the coordinates of point B are (15,9).