Question

Your friend claims there is an easier way to find the length of a segment than the Distance Formula when the x-coordinates of the endpoints are equal. He claims all you have to do is subtract the y-coordinates. In the image above, this would be like two hot air balloons directly in line with each other with one below and one above. Do you agree with his statement? Explain your reasoning. You may include an image, a graph, or work to help support your argument

Answer 1

Answer:

The statement is not correct.

Simply subtracting the $y$-coordinate does not ensure that we will have a nonnegative result.

Step-by-step explanation:

Given

To find the length of a segment than the Distance Formula when the x-coordinates of the endpoints are equal. He claims all you have to do is subtract the y-coordinates.

Step 1 of 2

Your friend is not correct.

We shall take note that distances are nonnegative.

Simply subtracting the $y$-coordinate does not ensure that we will have a nonnegative result.

Step 2 of 2

$A B &=\sqrt{\left(x_{1}-x_{2}\right)^{2}+\left(y_{1}-y_{2}\right)^{2}}$

$&=\sqrt{(x-x)^{2}+\left(y_{1}-y_{2}\right)^{2}}$

$&=\sqrt{0+\left(y_{1}-y_{2}\right)^{2}}$

$&=\sqrt{\left(y_{1}-y_{2}\right)^{2}}$

$A B &=\left|y_{1}-y_{2}\right|$

Therefore, if the $x$-coordinate of the endpoints are the same, then we can proceed by taking the absolute value of the difference of the $y$-coordinates to find the length of the segment.

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