Distance and Midpoint Formulas

Front

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

Back

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

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

Back

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

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 two points is 10 units, what could be the coordinates of these points?

Back

Examples: (0, 0) and (10, 0), or (3, 4) and (3, -6) etc.

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, -11) and (8, -42).

Back

Distance = √((8 - (-3))² + (-42 - (-11))²) = √((11)² + (-31)²) = √(121 + 961) = √1082 ≈ 32.9

Front

What is the y-coordinate of the midpoint of the line segment connecting (2, 4) and (6, 8)?

Back

Midpoint y-coordinate = (4 + 8)/2 = 6

Front

If the coordinates of point A are (x1, y1) and point B are (x2, y2), how do you find the x-coordinate of the midpoint?

Back

x-coordinate of Midpoint = (x1 + x2)/2