Question

6. Find the coordinates of P so that P partitions the segment AB in the ratio 5 to 2 if A(-8,-2) and B(6,5). 3,-6)

Answer 1

Using the formula for partitioning a segment in a given ratio, we have:

$\begin{gathered} X\text{ coordinate} \\ \frac{bx1+ax2}{a+b}(x1=-8,x2=6,a=5,b=2) \\ \frac{(2)(-8)+(5)(6)}{5+2}\text{ (Replacing)} \\ \frac{-16+30}{5+2}\text{ (Multiplying)} \\ \frac{-16+30}{7}(\text{Adding)} \\ \frac{14}{7}\text{ (Subtracting)} \\ \text{ The x-coordinate of P is 4/7} \end{gathered}$$\begin{gathered} Y\text{ Coordinate} \\ \frac{by1+ay2}{a+b}(y1=-2,y2=5,a=5,b=2) \\ \frac{(2)(-2)+(5)(5)}{5+2}\text{ (Replacing)} \\ \frac{-4+25}{5+2}\text{ (Multiplying)} \\ \frac{21}{7}(\text{Adding)} \\ \frac{21}{7}\text{ (Subtracting)} \\ \text{The y-coordinate of P is 21/7} \end{gathered}$