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 is commonly expressed as:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Where:
- d represents the distance between the two points,
- x1 and y1 are the coordinates of the first point,
- x2 and y2 are the coordinates of the second point,
- sqrt represents the square root function.
Now, to calculate the distance between A(1,1) and B(7,-7), we can plug in the values into the distance formula:
d = sqrt((7 - 1)^2 + (-7 - 1)^2)
= sqrt(6^2 + (-8)^2)
= sqrt(36 + 64)
= sqrt(100)
= 10
Therefore, the distance between 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 is derived from the Pythagorean theorem.
The distance formula is expressed as:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
where:
- d is the distance between the two points
- (x1, y1) are the coordinates of the first point
- (x2, y2) are the coordinates of the second point
To calculate the distance between point A(1,1) and point B(7,-7), we can substitute the coordinates into the formula:
d = sqrt((7 - 1)^2 + (-7 - 1)^2)
d = sqrt(6^2 + (-8)^2)
d = sqrt(36 + 64)
d = sqrt(100)
d = 10
Therefore, the distance between point A(1,1) and point B(7,-7) is 10 units.