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

Answer: (C)

(2, 0)

Answer 2

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 $(6, 0)$.