In cicrcle O, a diameter has endpoints (-5,4) and (3,-6). What is the length of the diameter?
Surely by the end of the semester of geometry, after a year of algebra, you have heard of the Pythagorean Theorem?
d^2 = (-5 - 3)^2 + (4 - -6)^2
d^2 = (-8)^2 + (10)^2
d^2 = 64+100 = 164
d = 12.806
To find the length of the diameter, we need to use the distance formula. The formula to find the distance between two points (x1, y1) and (x2, y2) is given by:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
In this case, the endpoints of the diameter are (-5,4) and (3,-6). Plugging these values into the distance formula, we get:
d = sqrt((3 - (-5))^2 + (-6 - 4)^2)
Simplifying further:
d = sqrt((3 + 5)^2 + (-6 - 4)^2)
d = sqrt(8^2 + (-10)^2)
d = sqrt(64 + 100)
d = sqrt(164)
d ≈ 12.81
Therefore, the length of the diameter is approximately 12.81 units.
To find the length of the diameter, we can use the distance formula between two points.
The distance formula is given by:
d = √[(x2 - x1)^2 + (y2 - y1)^2]
Let's label the coordinates of the two endpoints of the diameter as (x1, y1) = (-5, 4) and (x2, y2) = (3, -6).
Now, we can substitute these values into the formula:
d = √[(3 - (-5))^2 + (-6 - 4)^2]
Simplifying the expression inside the square root:
d = √[8^2 + (-10)^2]
d = √[64 + 100]
d = √164
Therefore, the length of the diameter is √164, which is approximately 12.81 (rounded to two decimal places).