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.
The distance formula is expressed as:
√((x₂ - x₁)² + (y₂ - y₁)²)
Where (x₁, y₁) and (x₂, y₂) are the coordinates of two points.
To calculate the distance between points A(1,1) and B(7,-7), we need to substitute the values into the distance formula.
Let's assign A's coordinates to (x₁, y₁) and B's coordinates to (x₂, y₂):
x₁ = 1
y₁ = 1
x₂ = 7
y₂ = -7
Now we apply the formula, substituting the values:
Distance = √((7 - 1)² + (-7 - 1)²)
Distance = √(6² + (-8)²)
Distance = √(36 + 64)
Distance = √100
Distance = 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.
The formula is as follows:
d = √[(x2 - x1)^2 + (y2 - y1)^2]
Where:
- d represents the distance between the two points
- (x1, y1) represents the coordinates of the first point
- (x2, y2) represents the coordinates of the second point
Now let's use this formula to calculate the distance between point A(1,1) and point B(7,-7).
We have:
- (x1, y1) = (1,1)
- (x2, y2) = (7,-7)
Substituting these values into the formula, we have:
d = √[(7 - 1)^2 + (-7 - 1)^2]
= √[6^2 + (-8)^2]
= √[36 + 64]
= √100
= 10
Therefore, the distance between point A(1,1) and point B(7,-7) is 10 units.