Distance Formula Review

Front

What is the distance formula used to calculate the distance between two points in a coordinate plane?

Back

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

Front

How do you simplify the expression √(41)?

Back

√(41) is already in its simplest form as 41 is not a perfect square.

Front

What is the distance between the points (1, 3) and (5, 6)?

Back

The distance is 5 units, calculated using the distance formula: d = √((5-1)² + (6-3)²) = √(16 + 9) = √25 = 5.

Front

What does the variable 'd' represent in the distance formula?

Back

In the distance formula, 'd' represents the distance between two points.

Front

If the coordinates of point A are (3, 2) and point B are (5, 6), how would you express the distance AB using the distance formula?

Back

AB = √((5 - 3)² + (6 - 2)²) = √(2² + 4²) = √(4 + 16) = √20.

Front

What is the first step in using the distance formula?

Back

The first step is to identify the coordinates of the two points you are measuring the distance between.

Front

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

Back

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

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, as distance cannot be negative.

Front

How can you verify your answer after calculating the distance between two points?

Back

You can verify your answer by checking the calculations step by step or using a graph to visually confirm the distance.

Front

What is the distance between the points (5, 0) and (3, 4)?

Back

The distance is √((3 - 5)² + (4 - 0)²) = √(4 + 16) = √20 = 4.47 units.