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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 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.
The distance formula in mathematics allows us to calculate the distance between two points in a coordinate plane. It is derived from the Pythagorean theorem and is represented as:
Distance = sqrt((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.
Step 1: Assign the coordinates of point A to x1 and y1, and the coordinates of point B to x2 and y2.
x1 = 1, y1 = 1
x2 = 7, y2 = -7
Step 2: Substitute the values into the distance formula.
Distance = sqrt((7 - 1)^2 + (-7 - 1)^2)
Step 3: Simplify the equation inside the square root.
Distance = sqrt(6^2 + (-8)^2)
Step 4: Calculate the squares and add them.
Distance = sqrt(36 + 64)
Step 5: Simplify the expression inside the square root.
Distance = sqrt(100)
Step 6: Take the square root of 100.
Distance = 10
Therefore, the distance between points A(1, 1) and B(7, -7) is 10 units.
The distance formula is a formula used to find the distance between two points in a coordinate plane. It is derived from the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
To calculate the distance between two points, A(x1, y1) and B(x2, y2), we can use the following formula:
Distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Now let's use this formula to calculate the distance between A(1, 1) and B(7, -7).
Step 1: Identify the coordinates of the two points.
A: x1 = 1, y1 = 1
B: x2 = 7, y2 = -7
Step 2: Plug the coordinates into the distance formula.
Distance = sqrt((7 - 1)^2 + (-7 - 1)^2)
Step 3: Simplify the formula.
Distance = sqrt(6^2 + (-8)^2)
Distance = sqrt(36 + 64)
Distance = sqrt(100)
Distance = 10
Therefore, the distance between A(1, 1) and B(7, -7) is 10 units.