Distance formula

Front

What is the distance formula?

Back

The distance formula is used to determine the distance between two points in a coordinate plane. It is given by the formula: d = √((x2 - x1)² + (y2 - y1)²).

Tags

CCSS.HSG.GPE.B.7

Front

How do you find the distance between the points (-4, 5) and (7, 18)?

Back

Using the distance formula: d = √((7 - (-4))² + (18 - 5)²) = √((11)² + (13)²) = √(121 + 169) = √290 ≈ 17.03.

Tags

CCSS.HSG.GPE.B.7

Front

What is the distance between the points (2, 3) and (5, 7)?

Back

Using the distance formula: d = √((5 - 2)² + (7 - 3)²) = √((3)² + (4)²) = √(9 + 16) = √25 = 5.

Tags

CCSS.HSG.GPE.B.7

Front

What does the term 'hypotenuse' refer to in a right triangle?

Back

The hypotenuse is the longest side of a right triangle, opposite the right angle.

Front

If the coordinates of point A are (1, 2) and point B are (4, 6), what is the distance between them?

Back

Using the distance formula: d = √((4 - 1)² + (6 - 2)²) = √((3)² + (4)²) = √(9 + 16) = √25 = 5.

Tags

CCSS.HSG.GPE.B.7

Front

What is the significance of the distance formula in geometry?

Back

The distance formula helps in calculating the length of line segments, determining if points are equidistant, and solving problems involving triangles and other geometric shapes.

Tags

CCSS.HSG.GPE.B.7

Front

How do you calculate the length of a side in a right triangle using the distance formula?

Back

Identify the coordinates of the endpoints of the side, then apply the distance formula to find the length.

Tags

CCSS.6.G.A.3

Front

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

Back

The distance formula is derived from the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Tags

CCSS.HSG.GPE.B.7

Front

Find the distance between the points (0, 0) and (3, 4).

Back

Using the distance formula: d = √((3 - 0)² + (4 - 0)²) = √(3² + 4²) = √(9 + 16) = √25 = 5.

Tags

CCSS.HSG.GPE.B.7

Front

What is the distance between the points (-1, -1) and (2, 2)?

Back

Using the distance formula: d = √((2 - (-1))² + (2 - (-1))²) = √((3)² + (3)²) = √(9 + 9) = √18 = 3√2.

Tags

CCSS.HSG.GPE.B.7