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

Problem:
We are given the diameter of a circle is 6 cm. One end of the diameter is at the point \((-4, 0)\), and the point lies on the x-axis. We are to find the other end of the diameter, which also lies on the x-axis.

Step 1: Understand the properties of a diameter
The diameter is a straight line segment passing through the center of the circle and connecting two points on the circle. If both ends lie on the x-axis, then their y-coordinates are both 0.

Let the other end of the diameter be \((x, 0)\).

Step 2: Use distance formula
The length of the diameter = distance between the two points = 6 cm
Use the distance formula between two points \((x_1, y_1)\) and \((x_2, y_2)\):
\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
Given one point: \((-4, 0)\) and the other point is \((x, 0)\)
Apply the distance formula:
\[ \sqrt{(x + 4)^2 + (0 - 0)^2} = 6 \Rightarrow \sqrt{(x + 4)^2} = 6 \Rightarrow |x + 4| = 6 \]
Solve for \(x\):
There are two cases for the modulus equation:
1) \(x + 4 = 6 \Rightarrow x = 2\)
2) \(x + 4 = -6 \Rightarrow x = -10\)

Step 3: Conclusion
So, the other end of the diameter can be at either of these points:
- \( (2, 0) \)
- \( (-10, 0) \)

Since both points are 6 cm away from \((-4, 0)\) and lie on the x-axis, both are mathematically valid solutions. However, typically in coordinate geometry, both points would be acceptable unless the context restricts to one.

Final Answer:
The other end of the diameter on the x-axis is at (2, 0) or (–10, 0).