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?

Question

asked May 17, 2021 233k views

2 Answers

Oliver Hnat · Answer 1 · 2021-05-23T10:11:56+0000

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.