Question

find the coordinates of Point P that lies on the segments MQ, M,-9 and -5 Q is 3,5 and partitions the segment out of ratio of 2 to 5

Answer 1

First, we need to find the distance between M (-9,-5) and Q (3,5)

`d=\sqrt[]{(-9-3)^2+(-5-5)^2}=\sqrt[]{(-12)^2+(-10)^2}=15.62`

then we need to know the distance of the point P

MP the distance is 4.46

PQ the distance is 11.157

we have the next equations

`4.46=\sqrt[]{(-9-x)^2+(-5-y)^2}`
`11.157=\sqrt[]{(3-x)^2+(5-y)^2}`

r=5/2=2.5

`x=(x1+rx2)/(1+r)=(-9+2.5(5))/(3.5)=(3.5)/(3.5)=1`
`y=(y1+ry2)/(1+r)=(-5+2.5(5))/(3.5)=2.14`