Question

Please Help!!! Locate the point on the line segment between (3,−5)and (13,−15)given that the point is 4/5of the way from to . Show your work.

Answer 1

`\boxed{P((67)/(9),-(85)/(9))}`

Step-by-step explanation:

Here we have the following points:

`A(3,-5) \\ \\ B(13,-15)`

So we want to know the point
`P` which is 4/5 of the way from A to B. So we can calculate this point as follows:

`P( \frac {mx_(\,2) + nx_(\,1) }{m + n},\frac {my_(\,2) + ny_(\,1) }{m + n} )`

Where:

`m:n=4:5 \\ \\ (x_(1),y_(1))=(3,-5) \\ \\ (x_(2),y_(2))=(13,-15) \\ \\ \\ Then: \\ \\ P( \frac {4(13) + 5(3)}{4+5},\frac {4(-15) + 5(-5) }{4+5} ) \\ \\ \boxed{P((67)/(9),-(85)/(9))}`