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