Distance and Midpoint

Front

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

Back

Distance = √((x2 - x1)² + (y2 - y1)²)

Front

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

Back

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

Front

What is the midpoint formula for two points (x1, y1) and (x2, y2)?

Back

Midpoint = ((x1 + x2)/2, (y1 + y2)/2)

Front

Find the midpoint of the points (2, 3) and (4, 7).

Back

Midpoint = ((2 + 4)/2, (3 + 7)/2) = (3, 5)

Front

What type of triangle does the Pythagorean Theorem apply to?

Back

Right triangle.

Front

If the coordinates of point A are (3, 4) and point B are (7, 1), what is the distance between A and B?

Back

Distance = √((7 - 3)² + (1 - 4)²) = √(16 + 9) = √25 = 5

Front

What is the significance of the Pythagorean Theorem in relation to distance?

Back

It relates the lengths of the sides of a right triangle to the distance between points.

Front

Calculate the distance between the points (-3, -11) and (8, -42).

Back

Distance = √((8 - (-3))² + (-42 - (-11))²) = √(121 + 961) = √1082 ≈ 32.9

Front

What is the distance between the points (-4, 5) and (7, 18)?

Back

Distance = √((7 - (-4))² + (18 - 5)²) = √(121 + 169) = √290 ≈ 17.03

Front

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

Back

Distance = √((x2 - x1)² + (y2 - y1)²)