Distance Formula and Midpoint Flashcard

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).

Front

What is the Midpoint Formula?

Back

The Midpoint Formula is used to find the midpoint between two points in a coordinate plane. It is given by the formula: M = ((x1 + x2)/2, (y1 + y2)/2).

Front

Calculate the distance between the points (1, 2) and (4, 6).

Back

d = √((4 - 1)² + (6 - 2)²) = √(3² + 4²) = √(9 + 16) = √25 = 5.

Front

What is the area of a rectangle with length 5 units and width 4 units?

Back

Area = length × width = 5 × 4 = 20 units squared.

Front

Find the distance between the points (2, 3) and (5, 7).

Back

d = √((5 - 2)² + (7 - 3)²) = √(3² + 4²) = √(9 + 16) = √25 = 5.

Front

What is the y-coordinate of the midpoint between (2, 3) and (4, 7)?

Back

Midpoint y-coordinate = (3 + 7)/2 = 10/2 = 5.

Front

Find the midpoint between the points (1, 1) and (3, 3).

Back

Midpoint = ((1 + 3)/2, (1 + 3)/2) = (2, 2).

Front

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

Back

d = √((2 - (-1))² + (2 - (-1))²) = √(3² + 3²) = √(9 + 9) = √18 = 3√2.

Front

Calculate the area of a triangle with base 6 units and height 4 units.

Back

Area = (1/2) × base × height = (1/2) × 6 × 4 = 12 units squared.

Front

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

Back

d = √((3 - 0)² + (4 - 0)²) = √(3² + 4²) = √(9 + 16) = √25 = 5.