Midpoint Formula

Front

What is the formula to find the x-coordinate of the midpoint between two points (x1, y1) and (x2, y2)?

Back

The formula is \( \frac{x_1 + x_2}{2} \).

Front

What is the formula to find the y-coordinate of the midpoint between two points (x1, y1) and (x2, y2)?

Back

The formula is \( \frac{y_1 + y_2}{2} \).

Front

Define the term 'midpoint' in the context of geometry.

Back

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

Front

Given the points (3, 9) and (5, 9), what is the x-coordinate of the midpoint?

Back

The x-coordinate of the midpoint is \( \frac{3 + 5}{2} = 4 \).

Front

Given the points (6, -6) and (-10, -10), what is the y-coordinate of the midpoint?

Back

The y-coordinate of the midpoint is \( \frac{-6 + (-10)}{2} = -8 \).

Front

What is the midpoint of the line segment connecting the points (-4, 4) and (-2, 2)?

Back

The midpoint is (\( \frac{-4 + (-2)}{2}, \frac{4 + 2}{2} \) = (-3, 3)).

Front

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

Back

The general formula is \( \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \).

Front

If the endpoints of a line segment are (a, b) and (c, d), how do you calculate the midpoint?

Back

You calculate the midpoint using the formula \( \left( \frac{a + c}{2}, \frac{b + d}{2} \right) \).

Front

What is the significance of the midpoint in geometry?

Back

The midpoint is significant as it represents the center point of a line segment, useful in various geometric constructions.

Front

How do you find the midpoint of a horizontal line segment?

Back

For a horizontal line segment, the y-coordinates are the same, so the midpoint is found using the x-coordinates: \( \left( \frac{x_1 + x_2}{2}, y_1 \right) \).