Question

Find point P that divides segment AB into a 2:3 ratio. The point should be closer to A. A(-3,1) and B(3,5). P = Answer Round your answer to the nearest tenth. Write your answer as a point using parenthesis and a comma (__,__). Do not use any spaces.

Answer 1

To solve this problem you must apply the proccedure shown below:

1. By definition, if the point $P$ divides $AB$ into a ratio a:b, this point is $\frac{a}{a+b}$ of the distance of the segment. Therefore, this is:

$\frac{a}{a+b} =\frac{2}{2+3} =\frac{2}{5}$

2. The x coordinate of the point, is:

$x1+\frac{a}{a+b} (x2-x1)=-3+\frac{2}{5}(3-(-3)) =-0.6$

3. The y coordinate is:

$y1+\frac{a}{a+b} (y2-y1)=1+\frac{2}{5} (5-1)=2.6$

The answer is: $P(-0.6, 2.6)$