How do i find the coordinates of point dividing a line segment externally in a given ratio?

Question

How do i find the coordinates of the point dividing the line segment joining the points (1,5) and (6,7) externally in the ration 2:3? I know the equation, but i have problems with drawing it. 

Answer 1

Plot the two points. Draw a segment connecting them. 

To divided the segment into the ratio of 2:3, the segment must be divided into 5 parts. The coordinates

shall be 2 parts from one endpoint and 3 parts form the other.

 

Notice that the x-coordinates are 5 units apart. So the point on the segment at x = 2 is one part from ( 1, 5 ),

at x = 3, two parts from ( 1, 5 ), at x = 3, three parts from ( 1, 5 ), and so on.

 

So the coordinate of the line when x = 2 shall divide the segment in the ratio 2:3.

 

Use the point-slope or the two-point formula to determine the equation of the line.

 

y = 2x/5 + 23/5, at x = 2

 

y = 4/5 + 23/5

y = 27/5

 

The coordinate that divides the segment in the ration of 2:4 is ( 2, 27/5 ).