Distance and Midpoint Formulas

Front

What is the Midpoint Formula?

Back

The Midpoint Formula is given by: \( M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \) where (x1, y1) and (x2, y2) are the endpoints of a line segment.

Front

How do you find the midpoint of the points (2, 3) and (4, 7)?

Back

Using the Midpoint Formula: \( M = \left( \frac{2 + 4}{2}, \frac{3 + 7}{2} \right) = (3, 5) \)

Front

What is the Distance Formula?

Back

The Distance Formula is given by: \( d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \) where (x1, y1) and (x2, y2) are two points in a plane.

Front

Calculate the distance between the points (1, 2) and (4, 6).

Back

Using the Distance Formula: \( d = \sqrt{(4 - 1)^2 + (6 - 2)^2} = \sqrt{9 + 16} = \sqrt{25} = 5 \)

Front

What is the significance of the Distance Formula in geometry?

Back

The Distance Formula is used to determine the length of a line segment between two points in a coordinate plane.

Front

Find the distance between the points (0, 0) and (3, 4).

Back

Using the Distance Formula: \( d = \sqrt{(3 - 0)^2 + (4 - 0)^2} = \sqrt{9 + 16} = \sqrt{25} = 5 \)

Front

What is the midpoint of the line segment connecting (-1, -1) and (3, 3)?

Back

Using the Midpoint Formula: \( M = \left( \frac{-1 + 3}{2}, \frac{-1 + 3}{2} \right) = (1, 1) \)

Front

If the endpoints of a line segment are (2, 5) and (8, 9), what is the midpoint?

Back

Using the Midpoint Formula: \( M = \left( \frac{2 + 8}{2}, \frac{5 + 9}{2} \right) = (5, 7) \)

Front

What is the distance between the points (-3, -11) and (8, -42)?

Back

Using the Distance Formula: \( d = \sqrt{(8 - (-3))^2 + (-42 - (-11))^2} = \sqrt{(11)^2 + (-31)^2} = \sqrt{121 + 961} = \sqrt{1082} \approx 32.9 \)

Front

How do you express the distance between two points in a coordinate plane?

Back

The distance is expressed using the Distance Formula: \( d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \)