Distance and Pythagorean Theorem Practice

Front

What is the distance formula?

Back

The distance formula is used to determine the distance between two points (x1, y1) and (x2, y2) in a coordinate plane. It is given by: \(d = \sqrt{(x2 - x1)^2 + (y2 - y1)^2}\)

Front

What is the Pythagorean Theorem?

Back

The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). It is expressed as: \(c^2 = a^2 + b^2\)

Front

Calculate the distance between points A(8,1) and B(-2,-5).

Back

Using the distance formula: \(d = \sqrt{((-2 - 8)^2 + (-5 - 1)^2)} = \sqrt{(100 + 36)} = \sqrt{136} \approx 11.7\)

Front

Calculate the distance between points A(5,0) and B(1,4).

Back

Using the distance formula: \(d = \sqrt{((1 - 5)^2 + (4 - 0)^2)} = \sqrt{(16 + 16)} = \sqrt{32} \approx 5.7\)

Front

If a right triangle has legs of lengths 3 and 4, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: \(c^2 = 3^2 + 4^2 = 9 + 16 = 25\) thus, \(c = 5\)

Front

What is the relationship between the distance formula and the Pythagorean Theorem?

Back

The distance formula is derived from the Pythagorean Theorem. It calculates the distance between two points by treating the difference in x-coordinates and y-coordinates as the two legs of a right triangle.

Front

Find the distance between points A(2,3) and B(2,7).

Back

Using the distance formula: \(d = \sqrt{((2 - 2)^2 + (7 - 3)^2)} = \sqrt{(0 + 16)} = 4\)

Front

Find the distance between points A(0,0) and B(6,8).

Back

Using the distance formula: \(d = \sqrt{((6 - 0)^2 + (8 - 0)^2)} = \sqrt{(36 + 64)} = \sqrt{100} = 10\)

Front

What is the distance between points A(-1,-1) and B(1,1)?

Back

Using the distance formula: \(d = \sqrt{((1 - (-1))^2 + (1 - (-1))^2)} = \sqrt{(4 + 4)} = \sqrt{8} \approx 2.83\)

Front

If the coordinates of point A are (x1, y1) and point B are (x2, y2), what is the formula for the distance?

Back

The distance between points A and B is given by: \(d = \sqrt{(x2 - x1)^2 + (y2 - y1)^2}\)