Question

Using the image below, find the x value for the point that divides the line segment AB into a ratio of 2:3.

Answer 1

You can divide the line segment into an arbitrary ratio by dividing the difference in the x coordinates and the difference in the y coordinates in that same ratio. If you take (5-(-4)) and divide it into 5 parts, then take 2 parts and add them to -4, you'll get the x coordinate of the point that is 2/5 of the way from A to B. If that's too confusing, and you want a formula,

\[x_{div} = \frac{d*x_1+c*x_2}{c+d}\]where the ratio is \(c:d\) and \(x_1\) is the x-coordinate of the point on the left and \(x_2\) is the x-coordinate of the point on the right. \(x_{div}\) will be the x-coordinate of the dividing point.