Question

The coordinates of points S and T are S(-5, 2) and T(13, 14). What are the coordinates of the point that is 1/3 of the way from S to T?

a) (1, 11)
b) (-1, 10)
c) (-1, 8)
d) (-3, 5)

Answer 1

The coordinates of the point that is 1/3 of the way from S to T are (1, 6).

Step-by-step explanation:

To find the point that is 1/3 of the way from S to T, we need to find the coordinates that are 1/3 of the way between the x-coordinates and the y-coordinates of S and T. The x-coordinate of the point is found by taking 1/3 of the difference between -5 and 13 and adding it to -5. The y-coordinate of the point is found by taking 1/3 of the difference between 2 and 14 and adding it to 2. To calculate:

x = -5 + (1/3)(13 - (-5)) = -5 + (1/3)(18) = -5 + 6 = 1

y = 2 + (1/3)(14 - 2) = 2 + (1/3)(12) = 2 + 4 = 6

So the coordinates of the point that is 1/3 of the way from S to T is (1, 6).