Question

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

Answer 1

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

$\frac{y_1-y_2}{x_1-x_2}$

$\frac{4-(-11)}{-10-14} = -\frac{15}{24}$

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

$y-y_1=m(x-x_1)$

$y-4= \frac{-15}{24}(x+10)$

$y - 4 = -\frac{15}{24}x - \frac{25}{4}$

$y = - \frac{5}{8}x - \frac{9}{4}$

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.

$y= \frac{(-5)(-2)}{8}- \frac{9}{4}=-1$

The answer is (-2,-1).