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.


`(y_1-y_2)/(x_1-x_2)`


`(4-(-11))/(-10-14) = -(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= (-15)/(24)(x+10)`


`y - 4 = -(15)/(24)x - (25)/(4)`


`y = - (5)/(8)x - (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= ((-5)(-2))/(8)- (9)/(4)=-1`

The answer is (-2,-1).