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.
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.
Related Questions
If A is a point on the y-axis whose ordinate is 5 and B is the point (-3, 1), then the length of AB is
8 units
5 units
3 units
25 units
The points A(9, 0), B(9, 6), C(-9, 6) and D(-9, 0) are the vertices of a
rectangle
square
rhombus
trapezium
Assertion (A): Two ordered pairs (a, b) and (c, d) are equal if a = c and b = d.
Reason (R): If a ≠ b, then (a, b) ≠ (b, a).
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).
Assertion (A): The point P(3, -5) lies in quadrant II and the point Q(-2, -1) lies in quadrant III.
Reason (R): The signs of a point in I, II, III and IV quadrants are respectively (+, +), (-, +), (-, -) and (+, -).
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).