Question

When deriving the distance formula, Eowyn starts with two points, A(x1,y1) and B(x2,y2). She then draws point C on a horizontal line from point A and a vertical line from point B, giving it coordinates (x2,y1). In doing so, she believes she created a right triangle, with right angle C, which allows her to use the Pythagorean Theorem. She lets AC=b and BC=a, which means that AB=c by definition of the hypotenuse.
Next, she uses the Ruler Postulate to state that a=|x2−x1| and b=|y2−y1|. Then, combining this information with the Pythagorean Theorem, she is able to use the Substitution Property of Equality to state that (x2−x1)2+(y2−y1)2=AB2. Finally, she applies the Square Root Property of Equality to find AB=(x2−x1)2+(y2−y1)2−−−−−−−−−−−−−−−−−−√. She is able to ignore the possible negative root since distance is always positive, by definition.

Which statement about Eowyn's derivation is the most accurate?

Answer 1

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