Question

The point P(3, 4) is reflected in the line y = x to point (a, b). Then:

Options

• a = b

• a − b = 1

• b − a = 1

• none of these

Answer 1

none of these

Explanation:

When a point (x, y) is reflected across the line y = x, the coordinates are swapped, resulting in the point (y, x).

Therefore, the reflection of P(3, 4) is (4, 3). So, a = 4 and b = 3.

Checking all the given options:

Option 1. a = b ⇒ 4 ≠ 3, which is false.

Option 2. a − b = 1 ⇒ 4 x 3 = 12 ≠ 1, which is false.

Option 3. b − a = 1 ⇒ 3 − 4 = −1 ≠ 1, which is false.