Distance on a Coordinate Plane (Pythagorean Theorem)

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: c² = a² + b².

Front

How do you calculate the distance between two points on a coordinate plane?

Back

To calculate the distance (d) between two points (x1, y1) and (x2, y2) on a coordinate plane, use the distance formula: d = √((x2 - x1)² + (y2 - y1)²).

Front

What is the distance between points (3, -5) and (3, -8)?

Back

3 units.

Front

What is the length of the missing side if one side is 4 and the hypotenuse is 8?

Back

x = 8.

Front

What is the length of the longest side of a rectangle with sides 8 units and 14 units?

Back

14 units.

Front

What is the distance between points (-7, 8) and (2, 8)?

Back

9 units.

Front

Find the distance between (-9, -1) and (-2, -6). Round to the nearest tenth.

Back

8.6.

Front

What does it mean for two points to be vertically aligned on a coordinate plane?

Back

Two points are vertically aligned if they have the same x-coordinate, meaning they lie on a vertical line.

Front

What does it mean for two points to be horizontally aligned on a coordinate plane?

Back

Two points are horizontally aligned if they have the same y-coordinate, meaning they lie on a horizontal line.

Front

What is the formula for the distance between two points in a vertical line?

Back

For points (x, y1) and (x, y2), the distance is |y2 - y1|.