Practicing Success

Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Three-dimensional Geometry

Question:

Statement-1 : The point A(3, 1, 6) is the mirror image of the point B(1, 3, 4) in the plane x - y + z = 5.

Statement-2 : The plane x - y + z = 5 bisects the line segment joining A (3, 1, 6) and B(1, 3, 4)

Options:

Statement 1 is True, Statement 2 is true; Statement 2 is a correct explanation for Statement 1.

Statement 1 is True, Statement 2 is True; Statement 2 is not a correct explanation for Statement 1.

Statement 1 is True, Statement 2 is False.

Statement 1 is False, Statement 2 is True.

Correct Answer:

Statement 1 is True, Statement 2 is True; Statement 2 is not a correct explanation for Statement 1.

Explanation:

The coordinates of the mid-point of AB are (2, 2, 5). Clearly, it lies on x - y + z = 5. So, statement-2 is true. Directions ratios of AB are proportional to 2, -2, 2 or 1, -1, 1 which are proportional to the direction ratios of normal to the plane.

So, A(3, 1, 6) is the mirror image of B(1, 3, 4). Hence, statement-1 is true. But, statement-2 is not a correct explanation for statement-1.