Distance on a Coordinate Plane

Front

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

Back

Distance = √((x2 - x1)² + (y2 - y1)²)

Front

What is the Pythagorean theorem?

Back

a² + b² = c², where c is the hypotenuse of a right triangle.

Front

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

Back

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

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

If the coordinates of point A are (2, 3) and point B are (5, 7), what is the distance between A and B?

Back

Distance = √((5 - 2)² + (7 - 3)²) = √(9 + 16) = √25 = 5.

Front

What is the significance of the square root in the distance formula?

Back

The square root ensures that the distance is a non-negative value.

Front

What is the relationship between the sides of a right triangle and the distance formula?

Back

The distance formula is derived from the Pythagorean theorem, which relates the sides of a right triangle.

Front

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

Back

Use the Pythagorean theorem: If you know two sides, you can find the third side.

Front

What is the distance between points (1, 2) and (4, 6)?

Back

Distance = √((4 - 1)² + (6 - 2)²) = √(9 + 16) = √25 = 5.

Front

What is the formula for calculating the hypotenuse in a right triangle?

Back

c = √(a² + b²), where a and b are the lengths of the other two sides.