Given:
A circle with its center at (0, -3).
To find:
The standard equation for the given circle.
Solution:
The standard form of a circle is , where (h, k) is the center of the circle and r is the radius of the circle.
The center of the given circle is at (0, -3).
We need to determine the radius of the circle. The center is at (0, -3) and a point with the same y coordinate is (3, -3).
The radius of the circle units.
So for the given circle, (h, k) is (0, -3) and r is 3 units.
So the equation becomes .
The standard equation for the circle is
increase by 0.5
increase by 0.25
decrease by 0.5
decrease by 0.25
centimeter units. Which of the following points could
also be a vertex of the square?
F. (−4, 0)
G. ( 0, 1)
H. ( 1,−1)
J. ( 4, 1)
K. ( 5, 0)
Answer: The required point that could also be a vertex of the square is K(5, 0).
Step-by-step explanation: Given that the sides of a square are 3 cm long and one vertex of the square is at (2,0) on a square coordinate grid marked in centimeter units.
We are to select the co-ordinates of the point that could also be a vertex of the square.
To be a vertex of the given square, the distance between the point and the vertex at (2, 0) must be 3 cm.
Now, we will be suing the distance formula to calculate the lengths of the segment from the point to the vertex (2, 0).
If the point is F(-4, 0), then the length of the line segment will be
If the point is G(0, 1), then the length of the line segment will be
If the point is H(1, -1), then the length of the line segment will be
If the point is J(4, 1), then the length of the line segment will be
If the point is K(5, 0), then the length of the line segment will be
Thus, the required point that could also be a vertex of the square is K(5, 0).