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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

Find The Coordinates Of Point P That Lies On The Segments MQ M9 And 5 Q Is 35 And Partitions The Segment Out Of Ratio Of 2 To 5 class=

Sagot :

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

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

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

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

r=5/2=2.5

[tex]x=\frac{x1+rx2}{1+r}=\frac{-9+2.5(5)}{3.5}=\frac{3.5}{3.5}=1[/tex][tex]y=\frac{y1+ry2}{1+r}=\frac{-5+2.5(5)}{3.5}=2.14[/tex]

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