Question

What are the coordinates of the point 3/4 of the way from X(1, -6) to Y(9, 10)?

Answer 1

`P(x,y) = (7,6)`

Explanation:

Given

`X = (1,-6)`

`Y = (9,10)`

`Point = (3)/(4)`

Required

Determine the coordinate of the point;

First, we need to determine the ratio of the point between X and Y

Represent the point with P

If the distance between point X and point P is
`(3)/(4)`,

The distance between point P and point Y will be
`1 - (3)/(4) = (1)/(4)`

`Ratio = XP : PY`

`Ratio = (3)/(4) : (1)/(4)`

Multiply through by 4

`Ratio = 3: 1`

Now, the coordinate of P can be calculated using

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

Where

`m:n = 3:1`

`(x_1,y_1) = (1,-6)`

`(x_2,y_2) = (9,10)`

Substitute these values in the formula above

`P(x,y) = ((3 * 9 + 1 * 1)/(3+1),(3 * 10 + 1 * -6)/(3+1))`

`P(x,y) = ((27 + 1)/(4),(30 -6)/(4))`

`P(x,y) = ((28)/(4),(24)/(4))`

`P(x,y) = (7,6)`