Answer: C) 14 inches
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Explanation:
There are three methods to solve this problem
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Method #1
Let point D be at the location (0,6). So this point is on line BC such that it cuts BC into two pieces of BD and DC.
BD is 7 inches long since it spans from x = -7 to x = 0
DC is also 7 inches long because it spans from x = 0 to x = 7
We can treat everything on line BC as if it was a number line.
So overall, BC = BD+DC = 7+7 = 14 inches
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Method #2
Because points B and C are on the same horizontal level, we can subtract the x coordinates of each point. We apply absolute value to ensure the result of subtraction is never negative.
|B-C| = |-7-7| = |-14| = 14
or
|C - B| = |7 - (-7)| = |7 + 7| = |14| = 14
The order of subtraction doesn't matter as long as you use absolute value.
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Method #3
We can use the distance formula to compute the distance from B(-7,6) to C(7,6)
So we'll make (x1,y1) = (-7,6) and (x2,y2) = (7,6)
Then we have the following steps
[tex]d = \text{Distance from B to C}\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(-7-7)^2 + (6-6)^2}\\\\d = \sqrt{(-14)^2 + (0)^2}\\\\d = \sqrt{196 + 0}\\\\d = \sqrt{196}\\\\d = 14\\\\[/tex]
The distance from B to C is 14 inches, which is the same as saying segment BC is 14 inches long.
The distance formula is overkill in my opinion, so method 1 or 2 might be the better option.
