Find the x and y coordinates.

Question

The endpoints of MN are M(-4,11) and N(8,-1). Point D lies on MN and divides MN into two parts with lengths in a ratio 1:3 from N to M.

Answer 1

Since we are dividing the line segment NM in a ratio of 1:3, ND is 1/4 of the length of NM and DM is 3/4 of the length of NM.

 

From N to M, the x coordinates decrease by 12, from 8 to -4.

 

   x-coordinate of D = 8 - (1/4)(12) = 5

 

From N to M, the y-coordinates increase by 12, from -1 to 11.

 

   y-coordinate of D = -1 + (1/4)(12) = 2

 

So, D = (5,2)