Assign 6- Distance Formula

Front

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

Back

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

Front

How do you calculate the distance between the points (1, 2) and (-7, 3)?

Back

Using the distance formula: d = √((-7 - 1)² + (3 - 2)²) = √(64 + 1) = √65.

Front

What is the distance between the points (−7, 7) and (−11, −5)?

Back

Using the distance formula: d = √((-11 - (-7))² + (-5 - 7)²) = √((-4)² + (-12)²) = √(16 + 144) = 4√10.

Front

Calculate the distance between the points (-13, -11) and (-10, -8).

Back

Using the distance formula: d = √((-10 - (-13))² + (-8 - (-11))²) = √(3² + 3²) = √(9 + 9) = 3√2.

Front

What is the distance between the points (2, -4) and (-8, -6)?

Back

Using the distance formula: d = √((-8 - 2)² + (-6 - (-4))²) = √((-10)² + (-2)²) = √(100 + 4) = 2√26.

Front

Find the distance between the points (12, 14) and (−6, 11).

Back

Using the distance formula: d = √((-6 - 12)² + (11 - 14)²) = √((-18)² + (-3)²) = √(324 + 9) = 3√37.

Front

What is the significance of the distance formula in geometry?

Back

The distance formula is significant as it allows us to determine the length of a line segment between two points in a coordinate plane, which is fundamental in geometry.

Front

What are the coordinates of the midpoint between two points (x1, y1) and (x2, y2)?

Back

The midpoint M is given by M = ((x1 + x2)/2, (y1 + y2)/2).

Front

How can the distance formula be derived from the Pythagorean theorem?

Back

The distance formula is derived from the Pythagorean theorem by considering the horizontal and vertical distances between two points as the legs of a right triangle, where the distance is the hypotenuse.

Front

What is the relationship between the distance formula and the concept of Euclidean space?

Back

The distance formula is a fundamental concept in Euclidean space, which defines the geometric properties of points, lines, and shapes based on the notion of distance.