Distance Formula Mastery

What is the Distance Formula in Geometry?

• sqrt((x2 - x1)^2 + (y2 - y1)^2)

• sqrt((x1 - x2)^2 + (y1 - y2)^2)

• sqrt((y2 - y1)^2 + (x2 - x1)^2)

• sqrt((x2 + x1)^2 + (y2 + y1)^2)

If two points are given as (x1, y1) and (x2, y2), how can you find the distance between them using the Distance Formula?

• sqrt((x1 - x2)^2 + (y1 - y2)^2)

• sqrt((y2 - y1)^2 + (x2 - x1)^2)

• sqrt((x2 - x1)^2 + (y2 - y1)^2)

• sqrt((x2 + x1)^2 + (y2 + y1)^2)

Explain the Pythagorean Theorem and its relation to the Distance Formula.

• The Distance Formula in coordinate geometry is derived from the Pythagorean Theorem. It calculates the distance between two points (x1, y1) and (x2, y2) in a plane as the square root of the sum of the squares of the differences in their x and y coordinates. The formula is √((x2 - x1)^2 + (y2 - y1)^2). This formula essentially represents the hypotenuse of a right triangle formed by the two points and the origin.

• The Pythagorean Theorem is only applicable to equilateral triangles.

• The Distance Formula is based on the principles of algebraic equations.

• The Pythagorean Theorem is used to calculate the area of a circle.

Solve for the distance between the points (3, 4) and (7, 1) using the Distance Formula.

• 3

• 2

• 8

• 5

If the coordinates of two points are (2, 5) and (8, 3), calculate the distance between them.

• 2*sqrt(10)

• 4*sqrt(5)

• 6*sqrt(13)

• 10*sqrt(2)

How can you apply algebraic manipulations to simplify the Distance Formula?

• Apply algebraic manipulations like expanding squares, combining like terms, and taking square roots.

• Divide by zero

• Apply trigonometric functions instead

• Use calculus principles

Find the distance between the points (-1, 2) and (5, -3) by applying the Distance Formula.

• sqrt(61)

• sqrt(53)

• sqrt(34)

• sqrt(45)

What are the steps involved in deriving the Distance Formula using the Pythagorean Theorem?

• d = (x2 - x1) + (y2 - y1)

• d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

• d = sqrt((x2 - x1) + (y2 - y1))

• d = (x2 - x1)^2 + (y2 - y1)^2

Calculate the distance between the points (0, 0) and (9, 12) using the Distance Formula.

• 20

• 10

• 18

• 15

In what scenarios would you use the Distance Formula in real-life applications?

• Using the Distance Formula to calculate cooking times for recipes

• Applying the Distance Formula to determine the speed of a moving object

• Distance Formula is used in scenarios like calculating distances on maps, determining line segment lengths in geometry, or measuring physical distances between locations.

• Using the Distance Formula to calculate the volume of a 3D shape