Midpoint and Distance Formula

Front

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

Back

The distance formula is d = √((x2 - x1)² + (y2 - y1)²).

Front

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

Back

The midpoint formula is M = ((x1 + x2)/2, (y1 + y2)/2).

Front

How do you calculate the perimeter of a rectangle given its vertices?

Back

To calculate the perimeter of a rectangle, add the lengths of all four sides. If the vertices are (x1, y1), (x2, y2), (x3, y3), and (x4, y4), the perimeter P = 2 * (length + width).

Front

What is the length of the diagonal of a rectangle with vertices at (0,0), (0,4), (3,0), and (3,4)?

Back

The length of the diagonal can be calculated using the distance formula. The diagonal is between (0,0) and (3,4), so d = √((3-0)² + (4-0)²) = √(9 + 16) = √25 = 5.

Front

What is the significance of the midpoint in geometry?

Back

The midpoint is the point that divides a line segment into two equal parts, and it is useful for finding the center of a segment.

Front

If the endpoints of a line segment are (1, 2) and (3, 4), what is the midpoint?

Back

The midpoint is M = ((1 + 3)/2, (2 + 4)/2) = (2, 3).

Front

What is the distance between the points (2, 3) and (5, 7)?

Back

Using the distance formula, d = √((5 - 2)² + (7 - 3)²) = √(3² + 4²) = √(9 + 16) = √25 = 5.

Front

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

Back

Add the x-coordinates and divide by 2 for the x-coordinate of the midpoint, and do the same for the y-coordinates.

Front

What is the perimeter of a rectangle with length 5 and width 3?

Back

The perimeter P = 2 * (length + width) = 2 * (5 + 3) = 2 * 8 = 16.

Front

If the endpoints of a segment are (4, 12) and (-6, 14), what is the midpoint?

Back

The midpoint is M = ((4 + (-6))/2, (12 + 14)/2) = (-1, 13).