Distance and Midpoint

Front

What is the definition of a midpoint in geometry?

Back

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

Front

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

Back

The midpoint M is calculated using the formula: M = (\frac{x1 + x2}{2}, \frac{y1 + y2}{2})

Front

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

Back

The distance d is calculated using the formula: d = \sqrt{(x2 - x1)^2 + (y2 - y1)^2}.

Front

If J is the midpoint of segment DK, what can be said about the lengths of DJ and JK?

Back

DJ = JK; the lengths are equal.

Front

What is the distance between the points (3, 4) and (7, 1)?

Back

The distance is \sqrt{(7 - 3)^2 + (1 - 4)^2} = \sqrt{16 + 9} = \sqrt{25} = 5.

Front

What is the significance of the midpoint in coordinate geometry?

Back

The midpoint helps in finding the center point of a line segment and is useful in various geometric constructions.

Front

If the coordinates of points A and B are (2, 3) and (8, 7), what is the midpoint?

Back

The midpoint is (\frac{2 + 8}{2}, \frac{3 + 7}{2}) = (5, 5).

Front

What is the distance between the points (-2, 7) and (6, -5)?

Back

The distance is \sqrt{(6 - (-2))^2 + (-5 - 7)^2} = \sqrt{(8)^2 + (-12)^2} = \sqrt{64 + 144} = \sqrt{208} = 4\sqrt{13}.

Front

What is the formula for finding the distance between two points in a 3D space?

Back

The distance d is calculated using the formula: d = \sqrt{(x2 - x1)^2 + (y2 - y1)^2 + (z2 - z1)^2}.

Front

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

Back

The distance is \sqrt{(3 - 1)^2 + (4 - 2)^2} = \sqrt{4 + 4} = \sqrt{8} = 2\sqrt{2}.