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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 mathematical equation that calculates the distance between two points in a coordinate plane. It is derived from the Pythagorean Theorem and is given by:
Distance = √((x2 - x1)² + (y2 - y1)²)
Where (x1, y1) and (x2, y2) are the coordinates of the two points.
To calculate the distance between A(1, 1) and B(7, -7), we can substitute the coordinates into the distance formula:
Distance = √((7 - 1)² + (-7 - 1)²)
= √(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 a mathematical formula used to calculate the distance between two points in a coordinate plane. It can be derived from the Pythagorean theorem.
The formula for calculating the distance between two points (x1, y1) and (x2, y2) is:
distance = √((x2 - x1)^2 + (y2 - y1)^2)
Now, let's calculate the distance between points A(1, 1) and B(7, -7) using the distance formula:
x1 = 1, y1 = 1
x2 = 7, y2 = -7
distance = √((7 - 1)^2 + (-7 - 1)^2)
distance = √(6^2 + (-8)^2)
distance = √(36 + 64)
distance = √100
distance = 10
So, the distance between points A(1, 1) and B(7, -7) is 10 units.