Explain the distance formula. Then use it to calculate the distance between A(1, 1) and B(7,−7).
The distance formula is a mathematical formula used to calculate the distance between two points in a coordinate plane. It is derived from the Pythagorean theorem and can be applied to any two-dimensional space.
The distance formula is given by:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Where:
- d represents the distance between the two points
- (x1, y1) are the coordinates of the first point
- (x2, y2) are the coordinates of the second point
- sqrt indicates the square root of the expression inside the parentheses
Now, let's calculate the distance between point A(1, 1) and point B(7, -7).
Substituting the coordinates into the formula:
d = sqrt((7 - 1)^2 + (-7 - 1)^2)
= sqrt((6)^2 + (-8)^2)
= sqrt(36 + 64)
= sqrt(100)
= 10
Therefore, the distance between points A(1, 1) and B(7, -7) is 10 units.
The distance formula is used to calculate the distance between two points in a coordinate plane. It can be determined using the coordinates of two points, (x₁, y₁) and (x₂, y₂), in the following way:
d = √((x₂ - x₁)² + (y₂ - y₁)²)
Now, let's use the distance formula to calculate the distance between point A(1, 1) and B(7, -7).
We have:
x₁ = 1
y₁ = 1
x₂ = 7
y₂ = -7
Substituting these values into the distance formula:
d = √((7 - 1)² + (-7 - 1)²)
= √(6² + (-8)²)
= √(36 + 64)
= √100
= 10
Therefore, the distance between point A(1, 1) and B(7, -7) is 10 units.
The distance formula is a mathematical equation used to calculate the distance between two points in a coordinate plane. It is derived from the Pythagorean theorem, which relates the sides of a right triangle. 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, and d represents the distance between them.
To calculate the distance between point A(1, 1) and B(7, -7), we substitute the values into the distance formula:
d = √[(7 - 1)^2 + (-7 - 1)^2]
Next, we simplify the equation:
d = √[6^2 + (-8)^2]
d = √[36 + 64]
d = √100
d = 10
Therefore, the distance between point A(1, 1) and B(7, -7) is 10 units.