Distance and Midpoint

Front

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

Back

Distance = √((x2 - x1)² + (y2 - y1)²)

Front

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

Back

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

Front

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

Back

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

Front

If point M(3, 4) is the midpoint of line segment AB, and point A is (-1, 6), what is the coordinates of point B?

Back

B = (2 * M - A) = (2 * (3, 4) - (-1, 6)) = (6 + 1, 8 - 6) = (7, 2).

Front

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

Back

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

Front

Find the midpoint of the segment with endpoints (4, 12) and (-6, 14).

Back

Midpoint = ((4 + (-6))/2, (12 + 14)/2) = (-1, 13).

Front

What does the distance formula represent in a coordinate plane?

Back

It represents the straight-line distance between two points.

Front

If the distance between points A(2, 3) and B(x, y) is 10, what is the equation that relates x and y?

Back

√((x - 2)² + (y - 3)²) = 10.

Front

What is the significance of the midpoint in geometry?

Back

The midpoint divides a line segment into two equal parts.

Front

Calculate the distance between the points (-3, -4) and (1, 2).

Back

Distance = √((1 - (-3))² + (2 - (-4))²) = √(16 + 36) = √52.