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 measure the distance between two points in a coordinate plane. It is derived from the Pythagorean theorem and can be used for any two-dimensional points.
The formula is as follows:
Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]
Where:
- (x₁, y₁) represents the coordinates of the first point.
- (x₂, y₂) represents the coordinates of the second point.
Now let's calculate the distance between points A(1, 1) and B(7, -7) using the distance formula:
Substituting the coordinates into the formula:
Distance = √[(7 - 1)² + (-7 - 1)²]
Simplifying:
Distance = √[6² + (-8)²]
= √[36 + 64]
= √100
= 10
Therefore, the distance between points A(1, 1) and B(7, -7) is 10 units.
The distance formula is used to find the distance between two points in a coordinate plane. It is based on the Pythagorean theorem. Here is the formula:
Distance = √[(x2 - x1)^2 + (y2 - y1)^2]
To calculate the distance between A(1, 1) and B(7, -7), we need to plug in the coordinates into the formula. Let's take A as (x1, y1) and B as (x2, y2):
x1 = 1
y1 = 1
x2 = 7
y2 = -7
Substituting these values into the formula, we get:
Distance = √[(7 - 1)^2 + (-7 - 1)^2]
= √[6^2 + (-8)^2]
= √[36 + 64]
= √100
= 10
Therefore, the distance between A(1, 1) and B(7, -7) is 10 units.