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 states that the distance between two points (x1, y1) and (x2, y2) is equal to the square root of the sum of the squared differences of their respective coordinates:
Distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)
To calculate the distance between points A(1, 1) and B(7, -7), we substitute the given coordinates into the distance formula:
Distance = sqrt((7 - 1)^2 + (-7 - 1)^2)
= sqrt((6)^2 + (-8)^2)
= sqrt(36 + 64)
= sqrt(100)
= 10
Therefore, the distance between points A and B is 10 units.
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Explain the distance formula. Then use it to calculate the distance between A(1, 1) and B(7,-7).
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