Question

Find the coordinates of the point 13 of the way from A to B. Segment A B plotted on a coordinate plane. Point A has coordinates negative 3 negative 2. Point B has coordinates 12 comma 4. Coordinates = ( , )

Answer 1

`(x,y) = (\¾, (5)/(2))`

Explanation:

Given

`Ratio = 1 :3`

`A = (-3, 2)`

`B = (12 , 4)`

Required

Determine the coordinates at the given ratio

This is calculated using the following formula

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

Where:

`m : n = 1 : 3`

Substitute values for x1, x2, y1, y2, m and n

`(x,y) = ((1 * 12 + 3 * -3)/(1 + 3),(1 * 4 + 3 * 2)/(1 + 3))`

`(x,y) = ((12-9)/(4),(4 + 6)/(4))`

`(x,y) = (\¾,(10)/(4))`

The coordinates is at point:
`(\¾, (5)/(2))`