distance formula two points

Front

What is the distance formula for two points in a coordinate plane?

Back

The distance formula is given by: d = √((x2 - x1)² + (y2 - y1)²), where (x1, y1) and (x2, y2) are the coordinates of the two points.

Front

Calculate the distance between the points (2, 4) and (6, 8).

Back

d = √((6 - 2)² + (8 - 4)²) = √(16 + 16) = √32 = 4√2.

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

d = √((4 - 1)² + (6 - 2)²) = √(9 + 16) = √25 = 5.

Front

What is the significance of the distance formula in real-life applications?

Back

The distance formula is used in various fields such as navigation, architecture, and computer graphics to calculate the shortest path between two points.

Front

How do you determine if three lengths can form a right triangle?

Back

Use the Pythagorean theorem: a² + b² = c², where c is the length of the hypotenuse.

Front

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

Back

d = √((3 - 0)² + (4 - 0)²) = √(9 + 16) = √25 = 5.

Front

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

Back

The distance formula is derived from the Pythagorean theorem, as it calculates the length of the hypotenuse of a right triangle formed by the two points.

Front

Estimate the distance between the points (1, 1) and (2, 2) using the distance formula.

Back

d = √((2 - 1)² + (2 - 1)²) = √(1 + 1) = √2.

Front

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

Back

d = √((0 - (-3))² + (0 - (-4))²) = √(9 + 16) = √25 = 5.