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:
d = √[(x2 - x1)^2 + (y2 - y1)^2]
Where:
- d represents the distance between the two points.
- (x1, y1) and (x2, y2) are the coordinates of the two points.
To calculate the distance between points A(1, 1) and B(7, -7), we substitute the coordinates into the distance formula:
d = √[(7 - 1)^2 + (-7 - 1)^2]
= √[(6)^2 + (-8)^2]
= √[36 + 64]
= √100
= 10
Therefore, the distance between A(1, 1) and B(7, -7) is 10 units.
The distance formula is used to calculate the distance between two points in a two-dimensional Cartesian coordinate system. It is derived from the Pythagorean theorem.
The distance formula is:
d = √((x2 - x1)^2 + (y2 - y1)^2)
To calculate the distance between points A(1, 1) and B(7, -7), we will use the distance formula.
First, we can assign the coordinates as follows:
x1 = 1
y1 = 1
x2 = 7
y2 = -7
Next, we substitute these values into the distance formula:
d = √((7 - 1)^2 + (-7 - 1)^2)
Simplifying:
d = √((6)^2 + (-8)^2)
d = √(36 + 64)
d = √100
d = 10.
Therefore, the distance between points A(1, 1) and B(7, -7) is 10 units.