Mathematics
Consider the following two statements:
Statement 1: The point (x2, y) lies on the y - axis. Then the value of x is zero.
Statement 2: The abscissa of every point on y-axis is zero.
Which of the following is valid?
Both the statements are true.
Both the statements are false.
Statement 1 is true, and Statement 2 is false.
Statement 1 is false, and Statement 2 is true.
Coordinate Geometry
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Answer
Any point that lies on the y-axis has its x-coordinate equal to zero.
The given point is (x2, y).
For this point to lie on the y-axis, its x-coordinate, which is x2, must be equal to zero.
So, x2 = 0.
If x2 = 0, then x must be 0.
∴ Statement 1 is true.
The abscissa is the x-coordinate of a point in a Cartesian coordinate system.
All points on the y-axis are of the form (0, y), where y can be any real number.
For any point on the y-axis, its x-coordinate (abscissa) is 0.
∴ Statement 2 is true.
∴ Both the statements are true.
Hence, option 1 is correct option.
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