Question

Segment AB is the diameter of a circle whose center is the point (2,5). If the coordinates of A are (1,3), find the

coordinates of B.

Answer 1

To find the coordinates of point B on the diameter of a circle with center (2, 5) and point A at (1, 3), we can use the midpoint formula to calculate the coordinates. The coordinates of point B are (3, 7).

Step-by-step explanation:

To find the coordinates of point B, we need to know that the center of the circle is the midpoint of segment AB. The midpoint formula can be used to find the coordinates of B. Let A be (x1, y1) and B be (x2, y2). Since the center of the circle is (2, 5) and A is (1, 3), we can use the midpoint formula:

((x1 + x2)/2, (y1 + y2)/2) = (2, 5)

Plugging in the values we have:

((1 + x2)/2, (3 + y2)/2) = (2, 5)

Solving for x2 and y2, we have:

1 + x2 = 4 --> x2 = 4 - 1 = 3

3 + y2 = 10 --> y2 = 10 - 3 = 7

Therefore, the coordinates of point B are (3, 7).

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