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Explain the distance formula. Then use it to calculate the distance between A(1, 1) and B(7,−7).
The distance formula is a formula used to calculate the distance between two points in a coordinate plane. It is derived from the Pythagorean theorem and can be defined as follows:
For two points A(x₁, y₁) and B(x₂, y₂), the distance between them is given by the formula:
Distance = √((x₂ - x₁)² + (y₂ - y₁)²)
To calculate the distance between A(1, 1) and B(7, -7), we can plug in the coordinates into the distance formula as follows:
Distance = √((7 - 1)² + (-7 - 1)²)
= √(6² + (-8)²)
= √(36 + 64)
= √100
= 10
Therefore, the distance between A(1, 1) and B(7, -7) is 10 units.