Pythagorean Theorem and Distance Formula

Front

What is the Pythagorean Theorem?

Back

The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). It can be expressed as: a² + b² = c².

Front

What is the Distance Formula?

Back

The Distance Formula is used to determine the distance between two points (x₁, y₁) and (x₂, y₂) in a coordinate plane. It is given by: d = √((x₂ - x₁)² + (y₂ - y₁)²).

Front

How do you find the length of a missing side in a right triangle?

Back

To find the length of a missing side in a right triangle, use the Pythagorean Theorem: a² + b² = c², where c is the hypotenuse and a and b are the other two sides.

Front

What is the formula for finding the midpoint between two points?

Back

The midpoint M between two points (x₁, y₁) and (x₂, y₂) is given by: M = ((x₁ + x₂)/2, (y₁ + y₂)/2).

Front

What is the opposite of squaring a number?

Back

The opposite of squaring a number is taking the square root of that number.

Front

If one side of a right triangle is 15 and the hypotenuse is 21, what is the length of the other side?

Back

Using the Pythagorean Theorem: 21² - 15² = x²; thus, x = 17.

Front

What is the value of x in the equation 21² - 15² = x²?

Back

x = 17.

Front

What is the first step to solve for x in the equation x² + 15² = 21²?

Back

Rearrange the equation to isolate x²: x² = 21² - 15².

Front

What does the term 'hypotenuse' refer to in a right triangle?

Back

The hypotenuse is the longest side of a right triangle, opposite the right angle.

Front

What is the significance of the Pythagorean Theorem in real-world applications?

Back

The Pythagorean Theorem is used in various fields such as architecture, engineering, and navigation to calculate distances and design structures.