A circle has a center at point C(2, -4) and a point on the circle is located at point P(2, 1). What is the length of the diameter of the circle?
the diameter is twice the distance between the points which is 5
2 sqrt (25) = 10
To find the length of the diameter of the circle, you need to calculate the distance between the center point (C) and the point on the circle (P).
The distance formula can be used to find the distance between two points on a coordinate plane:
Distance = √[(x2 - x1)^2 + (y2 - y1)^2]
In this case, the coordinates of the center point (C) are (2, -4) and the coordinates of the point on the circle (P) are (2, 1).
Using the distance formula, we can calculate the distance:
Distance = √[(2 - 2)^2 + (1 - (-4))^2]
= √[0^2 + (1 + 4)^2]
= √[0 + 5^2]
= √[0 + 25]
= √25
= 5
Therefore, the length of the diameter of the circle is 5 units.