Mathematics
Assertion (A): Two points A and B having coordinates (3, 3) and (-3, -3) respectively are joined. The line segment AB passes through the origin.
Reason (R): Origin is the point of intersection of the coordinate axes.
Assertion (A) is true, Reason (R) is false.
Assertion (A) is false, Reason (R) is true.
Both Assertion (A) and Reason (R) are true, and Reason (R) is the correct reason for Assertion (A).
Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct reason (or explanation) for Assertion (A).
Coordinate Geometry
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Answer
When a point (x,y) is reflected across the origin (0, 0), its new coordinates become (−x, −y). This transformation is also known as point symmetry with respect to the origin.
Point A has coordinates (3, 3).
If we reflect point A(3, 3) across the origin (0, 0), the coordinates of its reflected image would be (−3, −3).
The coordinates of the given point B are exactly (−3, −3).
Since point B is the exact reflection of point A across the origin, it means that the origin (0, 0) lies precisely on the straight line segment connecting point A and point B.
Therefore, the line segment AB passes through the origin.
∴ Assertion (A) is true.
Origin is the point of intersection of the coordinate axes.
This is the definition of the origin in a Cartesian coordinate system. It's the point where the x-axis and y-axis intersect, and its coordinates are (0, 0).
∴ Reason (R) is true.
∴ Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct reason (or explanation) for Assertion (A).
Hence, option 4 is the correct option.
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