ABCD is square in which A lies on positive y-axis and B lies on the positive x-axis. If D is the point (12, 17), then co-ordinate of C is

Options

A. (17, 12)
B. (17, 5)
C. (17, 16)
D. (15, 3)

Answer

To find the coordinates of point C in square ABCD, where A lies on the positive y-axis, B lies on the positive x-axis, and D is given as (12, 17), we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Coordinates of Points A and B**:
- Since A lies on the positive y-axis, its coordinates can be represented as (0, y_A).
- Since B lies on the positive x-axis, its coordinates can be represented as (x_B, 0).

2. **Understand the Properties of the Square**:
- In a square, all sides are equal, and the angles between adjacent sides are 90 degrees.
- The coordinates of D are given as (12, 17).

3. **Determine the Length of the Sides**:
- The distance from point D to the x-axis is the y-coordinate of D, which is 17.
- The distance from point D to the y-axis is the x-coordinate of D, which is 12.

4. **Use the Properties of the Square**:
- Since the square has equal sides, the distance from A to D (along the y-axis) must equal the distance from B to D (along the x-axis).
- Therefore, the length of each side of the square is equal to the distance from D to either axis.

5. **Calculate the Coordinates of Point C**:
- Point C will be directly opposite to point D in the square.
- The x-coordinate of C will be equal to the y-coordinate of D, which is 17.
- The y-coordinate of C will be equal to the x-coordinate of D, which is 12.
- Thus, the coordinates of point C are (17, 12).

### Final Answer:
The coordinates of point C are **(17, 12)**.

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