Mathematics
P is the point of intersection of the line 3x - 5y = 3 and x - axis.
Assertion (A): P is invariant with respect to given line.
Reason (R): Coordinates of P are (0, 1).
Assertion (A) is true, but Reason (R) is false.
Assertion (A) is false, but Reason (R) is true.
Both Assertion (A) and Reason (R) are correct, and Reason (R) is the correct reason for Assertion (A).
Both Assertion (A) and Reason (R) are correct, and Reason (R) is incorrect reason for Assertion (A).
Reflection
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Answer
We know that,
The y-coordinate of any point on x-axis equals to 0.
Substituting y = 0 into the equation 3x - 5y = 3, we get :
⇒ 3x - 5.0 = 3
⇒ 3x = 3
⇒ x = = 1
So the point of intersection is P(1, 0).
So, reason (R) is false.
A point is invariant with respect to a line if it lies on that line.
Since, P is the point of intersection of line 3x - 5y = 3 and x-axis, so it lies on line 3x - 5y = 3.
So, assertion (A) is true.
Thus, Assertion (A) is true, but Reason (R) is false.
Hence, option 1 is the correct option.
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