the coordinates of AB are A(6,-3) and B(18,3). what are the coordinates of the point that is 1/3 if the way from A to B

Question

the coordinates of AB are A(6,-3) and B(18,3). what are the coordinates of the point that is 1/3 if the way from A to B

Answer 1

Let P = (x,y) be the point.

x = 6 + (1/3)(18 - 6) = 10

y = -3 + (1/3)(3 - (-3)) = -1

P = (10, -1)

Answer 2

If (a,b) and (c,d0 are the co-ordinates of the endpoints of a line segment and you wish to find the co-ordinates of a point p% of the way from a to b, the formula is

[(1-p)a+pc,(1-p)b+pd)]

You can plug in the values given in your problem.

Please note that the formula comes from the geometric theorem often called the side-splitter theorem.