Glossary for Lesson 5-2: Distance

Right Triangle

A right triangle is a triangle with one right angle, or one angle that measures 90^{\circ}.
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The hypotenuse is the longest side of a right triangle.  It lies opposite the right angle. 

Pythagorean Theorem

The Pythagorean Theorem states that if a right triangle’s sides have lengths a, b, and c, where c is the longest side (the hypotenuse), then a, b, and c are related to one another according to the equation a^2+b^2=c^2.
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Square Root

If we have some number a, then a square root of a is any number b such that b^2=a.  In other words, multiplying b by itself gives a.  We can denote the square root of a quantity a by using a radical sign over a : \sqrt a.  By convention, \sqrt a denotes the positive square root of a.  For example, 3\cdot3=9, and -3\cdot-3=9 as well, but so \sqrt 9=3.  To indicate the negative square root, -3 in this case, we must write -\sqrt 9

nth Root

The nth root of a number a is some number b that, when raised to the nth power, equals a : If b^n=a , then b is an nth root of a.  For example, since 3^4=81, 3 is a fourth root of 81.  We can denote the nth root of a quantity a using a radical sign with a

Distance Formula

We can use the distance formula to find the distance between any two points on the coordinate plane.  If our points are (x_1, y_1) and (x_2, y_2) and we call the distance between them d, then we can say that d=\sqrt {(x_2-x_1)^2+(y_2-y_1)^2} . The distance formula treats the straight line connecting these two points as the hypotenuse of a right triangle, and it uses the Pythagorean Theorem to find the length of this line.