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 definition of the midpoint of a line segment?

Back

The midpoint is the point that divides the segment into two equal parts.

Front

If the coordinates of point A are (2, 3) and point B are (8, 7), what is the distance between A and B?

Back

Distance = √((8 - 2)² + (7 - 3)²) = √(36 + 16) = √52 = 2√13.

Front

What does it mean for two segments to be congruent?

Back

Two segments are congruent if they have the same length.

Front

How do you find the midpoint of a line segment with endpoints (x1, y1) and (x2, y2)?

Back

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

Front

What is 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 significance of the midpoint in geometry?

Back

The midpoint is significant as it helps in bisecting segments and finding center points.

Front

If point M is the midpoint of segment AB, and A is at (1, 2) and B is at (7, 8), what are the coordinates of M?

Back

M = ((1 + 7)/2, (2 + 8)/2) = (4, 5).

Front

What is the distance between the points (3, 4) and (3, 10)?

Back

Distance = √((3 - 3)² + (10 - 4)²) = √(0 + 36) = √36 = 6.

Front

What is the term for the longest side of a right triangle?

Back

Hypotenuse.