Question

What are the coordinates of the point LaTeX: \frac{3}{4}\:3 4of the way from A to B? coordinate plane with line segment AB. Point A is at -5, -4 and point b at -3, 3

Answer 1

Answer:
`\left((-7)/(2),(5)/(4)\right)`.

Explanation:

It is given that Point A is at (-5, -4) and point B at (-3, 3).

We need to find the coordinates of the point which is 3/4 of the way from A to B.

Let the required point be P.

`AP:AB=3:4`

`AP:PB=AP:(AB-AP)=3:(4-1)=3:1`

It means, point P divides segment AB in 3:1.

Section formula: If a point divides a line segment in m:n, then

`\left((mx_2+nx_1)/(m+n),(my_2+ny_1)/(m+n)\right)`

Using section formula, we get

`P=\left((3(-3)+1(-5))/(3+1),(3(3)+1(-4))/(3+1)\right)`

`P=\left((-9-5)/(4),(9-4)/(4)\right)`

`P=\left((-14)/(4),(5)/(4)\right)`

`P=\left((-7)/(2),(5)/(4)\right)`

Therefore, the required point is
`\left((-7)/(2),(5)/(4)\right)`.