# 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}.

### Hypotenuse

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.

### 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

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.