Point C will be the point where the segment connecting points A and B intersects the x-axis.
Note that AB has the shortest distance between A and B. Therefore, the distance AC+BC is minimized. The point C lies on the x -axis so its y -coordinate is 0. Since we cannot exactly state its x -coordinate, we will find it algebraically. Note that a segment is a part of a linear function.
The slope of the line is - 116. With this in mind, we can write the equation of the line in slope-intercept form.
y= -11/6x+ b
To find the y-intercept b, we can substitute either the point A or the point B into the equation. Let's use A(-1,7).
Now we can complete the equation of our line.
y= -11/6x+ 31/6
We already know that the y -coordinate of the point C is 0. To find its x -coordinate, let's substitute y=0 in the above equation.
