The endpoint of MP are M(2,1) and P(14,10). If point K partitions MP in aratio of MK:KP=3:2, what are the coordinates of K?

Answer 1

The ratio of 3 : 2 is a ratio of 3 equal parts to 2 equal parts. Thus once the line between the two points is divided into fifths then the point is at 3 parts to 2 parts. Between M and P there is 14 - 2 or 12 in the x direction and 10 - 1 or 9 in the y direction. The x coordinate is 3 times (12/5) and for the y coordiante is 3 times ( 9/5). Multipling through and simpling: x = 7 1/5 and y is 6 2/5. Adding these amount to the M coordinates to find the K coordinates: 2 + 7 1/5 or 9 1/5 and the y is 1 + 5 2/5 or 6 2/5. K is (9 1/5, 6 2/5).