Calculate Distances and Midpoints in Geometry

Front

What is the distance formula in a 2D coordinate system?

Back

Front

How do you find the midpoint of a line segment between two points?

Back

Front

Calculate the distance between the points P1(1, 2) and P2(4, 6).

Back

Front

Find the midpoint of the line segment joining P1(-2, 0) and P2(2, 4).

Back

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, which is fundamental in geometry for measuring distances.

Front

If P1(3, 4) and P2(3, 8), what is the distance between them?

Back

Since both points have the same x-coordinate, the distance is simply the difference in y-coordinates: d(P1, P2) = |8 - 4| = 4.

Front

What is the distance between the points P1(-1, -1) and P2(1, 1)?

Back

Front

How do you derive the distance formula from the Pythagorean theorem?

Back

The distance formula is derived from the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (distance) is equal to the sum of the squares of the other two sides (differences in x and y coordinates).

Front

Find the midpoint of the line segment joining P1(a, b) and P2(0, 0).

Back

Front

What is the distance between points P1(0, 0) and P2(0, 5)?

Back

The distance is simply the difference in y-coordinates: d(P1, P2) = |5 - 0| = 5.