Determining the Distance Between Two Points

Front

What is the formula to calculate the distance between two points in a coordinate plane?

Back

The distance d between two points (x1, y1) and (x2, y2) is given by the formula: d = √((x2 - x1)² + (y2 - y1)²).

Front

How do you find the distance between two points that have the same x-coordinate?

Back

If two points have the same x-coordinate, the distance between them is the absolute difference of their y-coordinates: d = |y2 - y1|.

Front

What is the distance between two points that have the same y-coordinate?

Back

If two points have the same y-coordinate, the distance between them is the absolute difference of their x-coordinates: d = |x2 - x1|.

Front

In a three-dimensional space, how is the distance between two points calculated?

Back

In three-dimensional space, the distance d between two points (x1, y1, z1) and (x2, y2, z2) is calculated using the formula: d = √((x2 - x1)² + (y2 - y1)² + (z2 - z1)²).

Front

What is the significance of absolute value in distance calculations?

Back

Absolute value is used in distance calculations to ensure that the distance is always a non-negative value, regardless of the order of the points.

Front

How do you calculate the vertical distance between two points in a coordinate system?

Back

The vertical distance between two points (x1, y1) and (x2, y2) is calculated as |y2 - y1|.

Front

How do you calculate the horizontal distance between two points in a coordinate system?

Back

The horizontal distance between two points (x1, y1) and (x2, y2) is calculated as |x2 - x1|.

Front

What is the distance between the points (3, 4) and (3, 10)?

Back

The distance is |10 - 4| = 6.

Front

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

Back

The distance is |3 - (-2)| = 5.

Front

If a kite is flying at a height of 30 feet and a toy is at the bottom of a pool 10 feet deep, what is the distance between them?

Back

The distance is 30 + 10 = 40 feet.