Distance and Midpoint Review

Front

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

Back

AB = √((x2 - x1)² + (y2 - y1)²)

Front

What is the term for the point that divides a line segment into two equal parts?

Back

Midpoint

Front

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

Back

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

Front

From which theorem is the distance formula derived?

Back

Pythagorean Theorem

Front

What is the average of the x-coordinates of the endpoints of a segment called?

Back

Mean or Average

Front

What is the geometric interpretation of the distance formula?

Back

It represents the length of the straight line connecting two points in a Cartesian plane.

Front

How do you calculate the distance between points (3, 4) and (7, 1)?

Back

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

Front

What are the coordinates of the midpoint of the segment connecting points (2, 3) and (4, 7)?

Back

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

Front

What is the significance of the midpoint in geometry?

Back

It is the point that equally divides a line segment into two congruent segments.

Front

What is the distance between the points (-1, -1) and (2, 3)?

Back

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