Question

Find the coordinates of the point P that lies along the directed line segment from

G(1,1) to H(8,1) and the partitions the segment in the ratio 1 to 3


PLEASE I'M GOING CRAZY... THESE ARE ALL THE POINTS I CAN GIVE

heres a helpful source


https://oercommons.s3.amazonaws.com/media/courseware/relatedresource/file/imth-6-1-9-6-1-coordinate_plane_plotter/index.html

Answer 1

The coordinate of point P(x,y) is,
`((11)/(4) ,1)`

Explanation:

Let the coordinate of the point P be (x,y) .

A point P divides a segment GH internally in the ratio m:n, to find the coordinate of point P we use the section formula :

The coordinate of point

`P(x,y) = ((mx_(2)+nx_(1))/(m+n) , (my_(2)+ny_(1))/(m+n))`

Then, to find the co-ordinates of the point P dividing the line segment GH joining two given points in a given ratio i.e m:n= 1:3.

Then,

`x= (mx_(2)+nx_(1))/(m+n)`

`x=(1\cdot 8+3\cdot 1)/(1+3) =(8+3)/(4)=(11)/(4)`.

For y:

`y= (my_(2)+ny_(1))/(m+n)`

`y=(1\cdot 1+3\cdot 1)/(1+3) =(1+3)/(4)=(4)/(4)=1`.

Therefore, the coordinate of point P(x,y) is,
`((11)/(4) ,1)`