Coordinate Plane & Pythagorean Theorem

Front

What is the coordinate plane?

Back

A two-dimensional surface formed by the intersection of a horizontal line (x-axis) and a vertical line (y-axis), used to locate points using ordered pairs (x, y).

Front

What is the Pythagorean Theorem?

Back

A mathematical principle stating 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): a² + b² = c².

Front

How do you calculate the distance between two points (x1, y1) and (x2, y2)?

Back

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

Front

What are the coordinates of the origin in the coordinate plane?

Back

(0, 0) is the origin, where the x-axis and y-axis intersect.

Front

What is a right triangle?

Back

A triangle that has one angle measuring 90 degrees.

Front

What is the hypotenuse of a right triangle?

Back

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

Front

If one side of a right triangle is 3 units and the other is 4 units, what is the length of the hypotenuse?

Back

5 units, calculated using the Pythagorean Theorem: 3² + 4² = 5².

Front

What is the distance between the points (2, 3) and (5, 7)?

Back

The distance is 5 units, calculated using the distance formula: d = √((5 - 2)² + (7 - 3)²) = √(9 + 16) = √25 = 5.

Front

What does it mean for a set of side lengths to form a right triangle?

Back

The side lengths must satisfy the Pythagorean Theorem: a² + b² = c², where c is the longest side.

Front

How do you round a number to the nearest hundredth?

Back

Look at the third decimal place; if it's 5 or more, round up the second decimal place by one.