Find the 1/3 point of a line when given to end points

Question

A: (1,7)

B: (10,4)

Find the 1/3 point.

Answer 1

(1,7), (10,4)

(10-1)/3 = 9/3 = 3

3 +1 = 4 = x coordinate of the point 1/3 of the line segment joining the two points

(4-7)/3 = -3/3 = -1

7-1=6 = the y coordinate of the point 1/3 of the line segment joning the two points

(3,6) is the solution

Answer 2

Point A: (1, 7)

Point B: (10, 4)

From point A to point B, the x coordinate goes from 1 to 10 (an increase of 9 units) and the y coordinate goes from 7 to 4 (a decrease of 3 units).

The one-third point of a line between these two points is therefore 1/3 the distance in both the x and y direction starting from A and going toward B.

Therefore the 1/3 point is:

(1 + (1/3)(9), 7 + (1/3)(-3)) =

(1 + 3, 7 -1) =

(4, 6)