Geometry---Finding the distance between 2 points

Front

What is the formula to calculate the distance between two points in a Cartesian 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 the points (3, 24) and (7, 56)?

Back

Using the distance formula: d = √((7 - 3)² + (56 - 24)²) = √(4² + 32²) = √(16 + 1024) = √1040 ≈ 32.2.

Front

What is the distance between the points (-5, -8) and (-1, -16)?

Back

Using the distance formula: d = √((-1 - (-5))² + (-16 - (-8))²) = √(4² + (-8)²) = √(16 + 64) = √80 ≈ 8.9.

Front

Calculate the distance between the points (-12, 1) and (12, -1).

Back

Using the distance formula: d = √((12 - (-12))² + (-1 - 1)²) = √(24² + (-2)²) = √(576 + 4) = √580 ≈ 24.08.

Front

What is the distance between the points (x1, y1) and (x2, y2) if x1 = 0, y1 = 0, x2 = 3, y2 = 4?

Back

Using the distance formula: d = √((3 - 0)² + (4 - 0)²) = √(3² + 4²) = √(9 + 16) = √25 = 5.

Front

What does the distance formula represent in geometry?

Back

The distance formula represents the length of the straight line connecting two points in a two-dimensional space.

Front

If the distance between two points is 11.7, what could be the coordinates of these points?

Back

There are many possible coordinates. For example, (0, 0) and (11.7, 0) or (5, 5) and (5, 5 + 11.7) are two pairs.

Front

What is the significance of the square root in the distance formula?

Back

The square root is used to ensure that the distance is a non-negative value, as distance cannot be negative.

Front

How can you determine if two points are the same using the distance formula?

Back

If the distance calculated using the distance formula is 0, then the two points are the same.

Front

What is the distance between the points (1, 2) and (1, 5)?

Back

Using the distance formula: d = √((1 - 1)² + (5 - 2)²) = √(0 + 3²) = √9 = 3.