233k views
2 votes
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?

What are the coordinates of point P on the directed line segment from A to B such-example-1
User Mrexodia
by
6.7k points

2 Answers

2 votes

Answer:

The answer is C

Explanation:

User Paul Mitchell
by
6.7k points
4 votes

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.

User Oliver Hnat
by
6.4k points