1,755 views
34 votes
34 votes
Find the coordinates of Point P on line segment AB, where point P partitions AB at a 2:3 ratio. A(-3,-4) and B(2,6)

User Toufikovich
by
2.5k points

1 Answer

23 votes
23 votes

We are asked to find the coordinates of a point in a line segment that lies at a 2:3 ratio.

If the ratio is a:b, then the coordinates of a point that lies at that ratio is:


P_x=x_1+((a)/(a+b))(x_2-x_1)
P_y=y_1+((a)/(a+b))(y_2-y_1)

Where


\begin{gathered} (x_1,y_1)\text{ } \\ (x_2,y_2) \end{gathered}

Are the extreme points.

First, we will find the "x" coordinate of the point by finding the length of the segment of the line that lies in the "x" direction by subtracting the "x" coordinates of the given points, like this:


D_x=2-(-3)=5

The "x" coordinate of P must lie at 2:3 ratio of this distance, that is, it must lie at the following point


P_x=-3+5((2)/(2+3))=-1

To find the "y" coordinate we do a similar process


D_y=6-(-4)=10

We find the "y" coordinate


P_y=-4+10((2)/(2+3))=0

The answer is P=(-1,0)

User Zanderwar
by
2.8k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.