Pythagorean Theorem and Distance on the Coordinate Plane

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 is expressed as: a² + b² = c².

Front

What is the formula to find the distance between two points (x1, y1) and (x2, y2) on a coordinate plane?

Back

The distance formula is: d = √((x2 - x1)² + (y2 - y1)²).

Front

If a right triangle has legs of lengths 6 and 8, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: c = √(6² + 8²) = √(36 + 64) = √100 = 10.

Front

What is the distance between the points (3, 4) and (7, 1)?

Back

Using the distance formula: d = √((7 - 3)² + (1 - 4)²) = √(4 + 9) = √13 ≈ 3.61.

Front

True or False: The Pythagorean Theorem can only be used for right triangles.

Back

True.

Front

What is the relationship between the sides of a right triangle according to the Pythagorean Theorem?

Back

The sum of the squares of the two shorter sides (legs) equals the square of the longest side (hypotenuse).

Front

If c = 97 and b = 72, what is a?

Back

Using the Pythagorean Theorem: a = √(c² - b²) = √(97² - 72²) = √(9409 - 5184) = √4225 = 65.

Front

How do you round the distance to the nearest hundredth?

Back

Look at the third decimal place: if it is 5 or more, round up the second decimal place by one; if it is less than 5, keep the second decimal place as is.

Front

If John walks 6 blocks North and 8 blocks West, how far is he from the starting point?

Back

Using the Pythagorean Theorem: d = √(6² + 8²) = √(36 + 64) = √100 = 10 blocks.

Front

What is the correct expression of the Pythagorean Theorem?

Back

a² + b² = c².