Find a formula that expresses the fact that P(x, y) is a distance 9 from the origin.
x^2 + y^2 = 81
To find a formula that expresses the fact that a point P(x, y) is a distance of 9 from the origin, we can use the distance formula. The distance between two points (x1, y1) and (x2, y2) on a coordinate plane is given by:
d = √((x2 - x1)^2 + (y2 - y1)^2)
In this case, the first point is the origin, which has coordinates (0, 0), and the second point is P(x, y). So we can write the distance formula as:
9 = √((x - 0)^2 + (y - 0)^2)
Simplifying further:
81 = (x^2 + y^2)
Therefore, the formula that expresses the fact that P(x, y) is a distance 9 from the origin is x^2 + y^2 = 81.
To find a formula that expresses the fact that a point P(x, y) is a distance of 9 from the origin, we can use the distance formula.
The distance formula is given by:
d = √((x2 - x1)^2 + (y2 - y1)^2)
In this case, we want to find the distance from the origin to the point P(x, y). The origin is (0, 0), so we can substitute these values into the formula:
d = √((x - 0)^2 + (y - 0)^2)
Simplifying further:
d = √(x^2 + y^2)
Since we know that the distance is 9, we can equate it to the formula:
9 = √(x^2 + y^2)
To remove the square root, we square both sides:
81 = x^2 + y^2
Therefore, the formula that expresses the fact that P(x, y) is a distance 9 from the origin is x^2 + y^2 = 81.