What is the point that lies 1/3 of the distance from (-10, 4) to (14, -11)

First lets find the slope of the line that connects the two points.





Now use the slope and one of the points to write the equation for the line in point-slope form.









The horizontal distance between the two points is 14 - (-10) = 24. We are looking for the point one-third of the way from the first point, so divide 24 by 3. The point that is a third past the first given point is 8 past x = -10. So the point has an x value of -2.

Plug x = -2 into the equation.



The answer is (-2,-1).

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