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

Back

Using the distance formula: d = √((-1 - (-5))² + (-16 - (-8))²) = √((4)² + (-8)²) = √(16 + 64) = √80 ≈ 8.9.

Tags

CCSS.HSG.GPE.B.7

Front

What is 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 significance of the distance formula in geometry?

Back

The distance formula helps in finding the length of a line segment between two points, which is essential in geometry for solving problems related to shapes, distances, and coordinates.

Tags

CCSS.HSG.GPE.B.7

Front

What are the coordinates of the midpoint between two points?

Back

The midpoint M between two points (x1, y1) and (x2, y2) is given by M = ((x1 + x2)/2, (y1 + y2)/2).

Tags

CCSS.HSG.GPE.B.6

Front

How do you find the distance between the points (3, 24) and (7, 56)?

Back

Using the distance formula: d = √((7 - 3)² + (56 - 24)²) = √((4)² + (32)²) = √(16 + 1024) = √1040 ≈ 32.2.

Tags

CCSS.HSG.GPE.B.7

Front

What is the Pythagorean theorem and how does it relate to the distance formula?

Back

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

Tags

CCSS.HSG.GPE.B.7

Front

What is the distance between the points (0, 0) and (x, y)?

Back

Using the distance formula: d = √((x - 0)² + (y - 0)²) = √(x² + y²).

Tags

CCSS.HSG.GPE.B.7

Front

If the distance between two points is 10 units, what could be the coordinates of those points?

Back

Possible coordinates could be (0, 0) and (10, 0), or (3, 4) and (3, 14), among many others, as long as they satisfy the distance formula.

Tags

CCSS.HSG.GPE.B.6

Front

What is the distance between the points (1, 2) and (4, 6)?

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