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

`B(x_2,y_2)= (20,12)`

Explanation:

Given

`A = (0,0)`

`Ratio; m : n = 1 : 3`

`Point\ at\ 1 : 3 = (5,3)`

Required

Coordinates of B

This question will be answered using line ratio formula;

`(x,y) = ((mx_2 + nx_1)/(m + n),(my_2 + ny_1)/(m + n))`

In this case:

`(x,y) = (5,3)`

`(x_1,y_1) = (0,0)`

`m : n = 1 : 3`

Solving for
`(x_2,y_2)`

`(x,y) = ((mx_2 + nx_1)/(m + n),(my_2 + ny_1)/(m + n))` becomes

`(5,3) = ((1 * x_2 + 3 * 0)/(1 + 3),(1 * y_2 + 3 * 0)/(1 + 3))`

`(5,3) = ((x_2 + 0)/(4),(y_2 + 0)/(4))`

`(5,3) = ((x_2)/(4),(y_2)/(4))`

Comparing the right hand side to the left;

`(x_2)/(4) = 5` -- (1)

`(y_2)/(4) = 3` -- (2)

Solving (1)

`x_2 = 5 * 4`

`x_2 = 20`

Solving (2)

`y_2 = 3 * 4`

`y_2 = 12`

Hence;

`B(x_2,y_2)= (20,12)`