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Big Ideas Math Integrated I, 2016 View details

2. Reflections

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Exercise 31 Page 557

Reflect either point in the x-axis.

C(-4,0)

Practice makes perfect

Let's begin by plotting 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 use B. We will use this reflection to calculate AC+B'C instead of AC+BC.

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 (-4,0), the distance AC+BC is minimized.