Pythagorean Theorem, Distance, and Midpoint

Front

What is the Pythagorean Theorem?

Back

The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). Formula: a² + b² = c².

Front

How do you calculate the distance between two points (x1, y1) and (x2, y2)?

Back

The distance d can be calculated using the formula: d = √((x2 - x1)² + (y2 - y1)²).

Front

What is the formula for finding the midpoint of a segment with endpoints (x1, y1) and (x2, y2)?

Back

The midpoint M can be found using the formula: M = ((x1 + x2)/2, (y1 + y2)/2).

Front

If the endpoints of a segment are (2, 3) and (10, 11), what is the midpoint?

Back

The midpoint is (6, 7).

Front

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

Back

The distance is 5 units.

Front

How do you find the endpoint of a segment if you know one endpoint and the midpoint?

Back

If A(x1, y1) is one endpoint and M(xm, ym) is the midpoint, the other endpoint B(x2, y2) can be found using: x2 = 2*xm - x1 and y2 = 2*ym - y1.

Front

What is the distance between the points (3, 4) and (3, -2)?

Back

The distance is 6 units.

Front

If the midpoint of a segment is (4, 5) and one endpoint is (2, 3), what is the other endpoint?

Back

The other endpoint is (6, 7).

Front

What is the distance between the points (0, 0) and (8, 6)?

Back

The distance is 10 units.

Front

If the endpoints of a segment are (1, 1) and (7, 5), what is the distance?

Back

The distance is 7.21 units.