Question

What are the coordinates of point P on the directed line segment from A to B such that P is One-fourth the length of the line segment from A to B?

Answer 1

The answer is C

Explanation:

Answer 2

Given:

The coordinates of the point A and B are (-5,-1) and (4,1)

The point P on the directed line segment from A to B such that P is One-fourth the length of the line segment from A to B.

Thus, we have;

`m=1` and
`m+n=4`

We need to determine the coordinates of the point P(x,y)

x - coordinates of the point P:

The x - coordinates of the point P can be determined using the formula,

`x=\left((m)/(m+n)\right)\left(x_(2)-x_(1)\right)+x_(1)`

Substituting the values, we get;

`x=\left((1)/(4)\right)\left(4+5\right)-5`

`x=(9)/(4)-5`

`x=-(11)/(4)`

Thus, the x - coordinate of the point P is
`-(11)/(4)`

y - coordinate of the point P:

The y - coordinate of the point P can be determined using the formula,

`y=\left((m)/(m+n)\right)\left(y_(2)-y_(1)\right)+y_(1)`

Substituting the values, we get;

`y=\left((1)/(4)\right)\left(1+1\right)-1`

`y=(2)/(4)-1`

`y=(-2)/(4)`

`y=-(1)/(2)`

Thus, the y - coordinate of the point P is
`-(1)/(2)`

Therefore, the coordinates of the point P is
`\left((-11)/(4), (-1)/(2)\right)`

Hence, Option C is the correct answer.