Question

What are the coordinates of the point on the directed line segment from (-5,-4) to (9,8) that partitions the segment into a ratio of 3 to 1?

Answer 1

In this case, we'll have to carry out several steps to find the solution.

Step 01:

Segment

(-5,-4) ==> (9,8)

ratio = 3: 1

coordinates = ?

Step 02:

The midpoint formula

(-5,-4) ==> (9,8)

midpoint = ( (x1 + x2) / 2 , (y1 + y2) / 2 )

midpoint = ( (-5 + 9)/2 , (-4+9)/2 )

midpoint = ( 4/2 , 5/2 ) = ( 2 , 5/2)

( 2 , 5/2) ===> (9,8)

midpoint = ( (x1 + x2) / 2 , (y1 + y2) / 2 )

midpoint = ( (2+9)/2 , (5/2 + 8)/2 )

midpoint = ( 11/2 , 21/4) = ( 5.5 , 5.25)

The answer is:

The coordinates of the point are ( 11/2 , 21/4) = ( 5.5 , 5.25)