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Mathematics

Assertion (A): The graph of 2x = 1 is a line parallel to y-axis.

Reason (R): The equations of the form x = ± k are always parallel to y-axis.

  1. A is true, R is false.
  2. A is false, R is true.
  3. Both A and R are true.
  4. Both A and R are false.

Coordinate Geometry

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Answer

Both A and R are true.

Explanation

Given, 2x = 1

x = 12\dfrac{1}{2}

This represents a vertical line (parallel to the y-axis) because the value of x remains constant at 12\dfrac{1}{2} for all values of y.

This line is at a distance of 12\dfrac{1}{2} units to the right of the y-axis because the x-coordinate of every point on the line is 12\dfrac{1}{2}, which is 12\dfrac{1}{2} units in the positive direction along the x-axis.

∴ Assertion (A) is true.

For equations of the form x = ± k.

These represent vertical lines (parallel to the y-axis) because the value of x remains constant at k or -k for all values of y.

∴ Reason (R) is true.

Hence, both Assertion (A) and Reason (R) are true.

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