Reflect either point in the x-axis to find the third corner of a triangle.
C(5,0)
Practice makes perfect
We are given two points.
A(1,4) and B(6,1)
We want to find a point C on the x-axis so that AC+BC is the minimum distance. To do so, let's begin by drawing the two given points.
To find the point on the x-axis that will minimize the expression AC+CB, we can reflect either point in the x-axis. Let's start with point B. We will use this reflection to calculate AC+B'C instead of AC+BC.
Note that the image of B after the reflection is at the same distance of the x-axis as B. 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'. Additionally, because reflections maintain distance on either side of the line of reflection, BC=BC'. Therefore, if C has the coordinates (5,0), the distance AC+CB is minimized.
