Question

12. A circle has a center at C(2,5) and a point on the circle has coordinates A(8, 13). Could the point B lie on

the same circle if lies at B(9.1)? Justify.

Answer 1

After calculating the distances from the center C(2,5) to A(8,13) and B(9,1), we find that they are not the same, which means point B cannot lie on the same circle as point A with the specified center C.

Step-by-step explanation:

To determine if point B(9,1) could lie on the same circle as the points C(2,5) and A(8, 13), we need to compare the distances from C to both A and B. The distance between two points (x1, y1) and (x2, y2) is given by the distance formula: √((x2-x1)² + (y2-y1)²).

First, we calculate the distance from C to A:

√((8-2)² + (13-5)²) = √(6² + 8²) = √(36 + 64) = √100 = 10 units

Now, we calculate the distance from C to B:

√((9-2)² + (1-5)²) = √(7² + (-4)²) = √(49 + 16) = √65 ≈ 8.06 units

Since the distances from C to A and C to B are not the same (10 units vs. approximately 8.06 units), point B does not lie on the same circle as point A with the center at C, because all points on a circle's circumference are equidistant from its center.

Answer 2

No.

Step-by-step explanation:

A circle is defined as a figure in which all points are equidistant from the center, or C. In order to determine how far points A and B are from the center, we must first find the difference in positioning from (2,5) to each point and then use Pythagorean Theorem to calculate the length of the hypotenuse. Point A establishes that the radius of the circle must be 10 units, and Point Bis only about 8 units away.