Distance Between Points

Front

What is the formula to calculate the distance between two points (x1, y1) and (x2, y2)?

Back

The distance d is given by the formula: d = √((x2 - x1)² + (y2 - y1)²).

Tags

CCSS.HSG.GPE.B.7

Front

How do you find the midpoint of a line segment between two points (x1, y1) and (x2, y2)?

Back

The midpoint M is calculated as: M = ((x1 + x2)/2, (y1 + y2)/2).

Tags

CCSS.HSG.GPE.B.6

Front

What is the distance between the points (0, 0) and (3, 4)?

Back

The distance is 5, calculated using the distance formula: d = √((3 - 0)² + (4 - 0)²) = √(9 + 16) = √25 = 5.

Tags

CCSS.HSG.GPE.B.7

Front

What is the distance between the points (4, 5) and (-12, 5)?

Back

The distance is 16, calculated as: d = √((-12 - 4)² + (5 - 5)²) = √((-16)²) = √256 = 16.

Tags

CCSS.HSG.GPE.B.7

Front

What is the midpoint of the line segment from (2, 4) to (2, 8)?

Back

The midpoint is (2, 6), calculated as: M = ((2 + 2)/2, (4 + 8)/2) = (2, 6).

Tags

CCSS.HSG.GPE.B.6

Front

What is the distance between the points (1, 1) and (4, 5)?

Back

The distance is approximately 5.0, calculated as: d = √((4 - 1)² + (5 - 1)²) = √(9 + 16) = √25 = 5.

Tags

CCSS.HSG.GPE.B.7

Front

How do you calculate the distance between two points in a coordinate plane?

Back

Use the distance formula: d = √((x2 - x1)² + (y2 - y1)²).

Tags

CCSS.HSG.GPE.B.7

Front

What is the significance of the midpoint in geometry?

Back

The midpoint divides a line segment into two equal parts and is used in various geometric constructions.

Tags

CCSS.HSG.GPE.B.6

Front

What is the distance between the points (3, 3) and (7, 1)?

Back

The distance is approximately 4.47, calculated as: d = √((7 - 3)² + (1 - 3)²) = √(16 + 4) = √20 ≈ 4.47.

Tags

CCSS.HSG.GPE.B.7

Front

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

Back

The distance is approximately 4.24, calculated as: d = √((2 - (-1))² + (2 - (-1))²) = √(9 + 9) = √18 ≈ 4.24.

Tags

CCSS.HSG.GPE.B.7