Distance Formula Review Warm-Up

Front

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

Back

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

Front

How do you write the coordinates of point A(3,1) and point B(-2,-1) in the distance formula?

Back

The distance between points A(3,1) and B(-2,-1) is written as: d = √((-2 - 3)² + (-1 - 1)²).

Front

What is the distance between the points (-5, -8) and (-1, -16)?

Back

The distance is approximately 8.9.

Front

How is the distance formula derived from the Pythagorean theorem?

Back

The distance formula is derived by considering the distance between two points as the hypotenuse of a right triangle formed by the differences in their x and y coordinates.

Front

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

Back

The square root is used to ensure that the distance is a non-negative value, as distance cannot be negative.

Front

If point A is at (2,0) and point B is at (-2,4), how is the distance written?

Back

The distance is written as: d = √((-2 - 2)² + (4 - 0)²).

Front

What is the result of the distance calculation for points A(2,0) and B(-2,4)?

Back

The distance is approximately 4.47.

Front

What does each variable in the distance formula represent?

Back

In the distance formula d = √((x₂ - x₁)² + (y₂ - y₁)²), x₁ and y₁ are the coordinates of the first point, and x₂ and y₂ are the coordinates of the second point.

Front

How can you verify the distance calculated using the distance formula?

Back

You can verify the distance by plotting the points on a graph and measuring the distance directly or by using a ruler.

Front

What is the geometric interpretation of the distance formula?

Back

The distance formula represents the length of the straight line connecting two points in a two-dimensional space.