Question

The diameter of a circle is of length 6 cm. If one end of the diameter is \((-4, 0)\), the other end on \(x\)-axis is at:

• A. (0, 2)
• B. (6, 0)
• C. (2, 0)
• D. (4, 0)

Answer 1

The Correct Option is C

Given that the length of the diameter is 6 cm, we know that the midpoint of the diameter will be the center of the circle. One end of the diameter is given as \((-4, 0)\).

The other end of the diameter lies on the \(x\)-axis. The \(x\)-coordinate of the other end can be calculated by adding the diameter length to the \(x\)-coordinate of the first point since the line lies along the \(x\)-axis.

The center of the circle will be the midpoint between the two ends, which is calculated as the average of the \(x\)-coordinates and \(y\)-coordinates of the two ends:

\[ \text{Midpoint} = \left(\frac{-4 + x}{2}, \frac{0 + 0}{2}\right) \]

Since the midpoint lies at \((1, 0)\) because the radius is half of the diameter (i.e., 3 cm), we can set:

\[ \frac{-4 + x}{2} = 1 \]

Solving for \(x\):

\[ -4 + x = 2 \implies x = 6 \]

Thus, the other end of the diameter is \((6, 0)\).