Distance Formula Worksheet with Answers

Are you a high school or college student studying geometry? If so, you know the importance of mastering key concepts such as the distance formula. To help you practice and reinforce your understanding, we have put together a distance formula worksheet with answers. This worksheet provides a collection of problems that allow you to calculate the distance between two points on a coordinate plane. By working through these exercises, you can develop your skills and boost your confidence in solving distance-related problems.

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What is the distance between two points (2, 3) and (5, 1)?

To calculate the distance between two points (2, 3) and (5, 1), you can use the distance formula which is the square root of the sum of the squares of the differences in the x and y coordinates. So, the distance between the two points is ?((5-2)^2 + (1-3)^2) = ?(3^2 + (-2)^2) = ?(9 + 4) = ?13 units.

How do you find the distance between two points using the distance formula?

To find the distance between two points using the distance formula, you first identify the coordinates of the two points (x1, y1) and (x2, y2). Then, you plug these values into the distance formula: distance = ?((x2 - x1)² + (y2 - y1)²). Finally, calculate the square root of the sum of the squared differences in x and y coordinates to determine the distance between the two points.

What is the distance between (9, 6) and (-3, 4)?

The distance between the points (9, 6) and (-3, 4) is 12.21 units. This can be calculated using the distance formula: ?[(9 - (-3))^2 + (6 - 4)^2] = ?(144 + 4) = ?148 ? 12.21.

Which coordinates represent Point A and Point B in the distance formula?

In the distance formula, Point A is represented by the coordinates (x?, y?) and Point B is represented by the coordinates (x?, y?).

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

To calculate the distance between two points on a coordinate plane using the Pythagorean theorem, you would first identify the coordinates of the two points. Then, you would subtract the x-coordinates to find the horizontal distance and the y-coordinates to find the vertical distance. Next, square each of these distances, sum the squared values, and finally, take the square root of the sum to find the distance between the two points. This process is based on the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

What is the distance between (0, 0) and (10, 10)?

The distance between the points (0, 0) and (10, 10) is approximately 14.14 units, which can be calculated using the Pythagorean theorem: sqrt((10-0)^2 + (10-0)^2) = sqrt(10^2 + 10^2) = sqrt(200) ? 14.14 units.

What are the values of x and y in the distance formula for (x1, y1) and (x2, y2)?

In the distance formula for two points (x1, y1) and (x2, y2), the values of x and y are represented as (x2 - x1) and (y2 - y1), respectively. These differences in x and y coordinates are squared, summed, and then the square root is taken to find the distance between the two points.

How can the distance formula be used to find the length of a line segment?

The distance formula, \(\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\), can be used to find the length of a line segment by calculating the square root of the sum of the squares of the differences between the x-coordinates and y-coordinates of the two endpoints of the line segment. This formula essentially measures the straight-line distance between the two points, which represents the length of the line segment.

Calculate the distance between (4, 5) and (1, 2) using the distance formula.

To calculate the distance between the points (4, 5) and (1, 2) using the distance formula, we can use the formula: d = ?((x2 - x1)² + (y2 - y1)²). Substituting the coordinates into the formula, we get d = ?((1 - 4)² + (2 - 5)²) = ?((-3)² + (-3)²) = ?(9 + 9) = ?18 ? 4.24 units. Therefore, the distance between the two points is approximately 4.24 units.

Explain how the distance formula can be used to find the distance between two points in three-dimensional space.

In three-dimensional space, the distance formula can be used to find the distance between two points by calculating the square root of the sum of the squares of the differences in the coordinates of the points along the three axes. Mathematically, the formula is: distance = sqrt((x2 - x1)^2 + (y2 - y1)^2 + (z2 - z1)^2). This formula calculates the straight line distance between the two points in three-dimensional space.