1.
The ordinate of all the points on the x-axis is:
Correct Answer
A. 0
Explanation
The ordinate of a point on the x-axis represents its vertical distance from the origin. Since all points on the x-axis lie on the same vertical line, their vertical distance from the origin is always 0. Therefore, the correct answer is 0.
2.
If the x-coordinate of a point is zero, then this point lies:
Correct Answer
D. On y-axis
Explanation
If the x-coordinate of a point is zero, it means that the point lies on the y-axis. This is because the y-axis is a vertical line where the x-coordinate is always zero. Therefore, the given point lies on the y-axis.
3.
If the perpendicular distance of a point P from the x-axis is 7 units and the foot of the perpendicular lies on the negative direction of the x-axis, then the point P has:
Correct Answer
A. y-coordinate = 7 or –7 only
Explanation
The given information states that the point P has a perpendicular distance of 7 units from the x-axis and the foot of the perpendicular lies on the negative direction of the x-axis. This means that the point P can lie either above the x-axis or below it, hence the y-coordinate can be either positive 7 or negative 7. Therefore, the correct answer is "y-coordinate = 7 or -7 only".
4.
If P (–3, 8), Q (7, –5), R (–3, –8) and T (–7, 9) are four points in the Cartesian plane. Then the point(s) in the third quadrant are:
Correct Answer
C. Only R
Explanation
The point R is the only point in the third quadrant because it has negative x and y coordinates. P and T are not in the third quadrant because P has a negative x coordinate and a positive y coordinate, and T has a negative y coordinate and a negative x coordinate. Q is not in the third quadrant because it has a positive x coordinate and a negative y coordinate.
5.
The coordinates of any point on the y-axis are of the form (0, k), where |k| is the distance of the point from the:
Correct Answer
B. X-axis
Explanation
The coordinates of any point on the y-axis are of the form (0, k), where |k| is the distance of the point from the X-axis. This is because the y-axis is a vertical line that passes through the point (0,0), which is the origin. Therefore, the distance of any point on the y-axis from the X-axis is always 0.
6.
Which point lies to the right of y-axis?
Correct Answer
C. (3.5)
Explanation
The point (3.5) lies to the right of the y-axis because it only has an x-coordinate and no y-coordinate. In a Cartesian coordinate system, the y-axis is the vertical line that divides the plane into two halves. Points to the right of the y-axis have positive x-coordinates, while points to the left have negative x-coordinates. Since the point (3.5) does not have a y-coordinate and only an x-coordinate of 3.5, it is located to the right of the y-axis.
7.
For x=3, y= 2, u= 9, v=-13 the point ( x+y, u+v) lies in the ----- quadrant
Correct Answer
D. IV
Explanation
The point (x+y, u+v) can be calculated as (3+2, 9+(-13)) = (5, -4). In the coordinate plane, the x-axis represents the horizontal axis and the y-axis represents the vertical axis. The point (5, -4) lies in the fourth quadrant because both the x-coordinate and y-coordinate are positive.
8.
On joining the points (0,0), (0,2), (2,2) and (2,0) we obtain a
Correct Answer
A. A square
Explanation
The given points form a square because all four sides are equal in length and all four angles are right angles. A square is a type of quadrilateral where all sides are equal and all angles are right angles.
9.
The point at which the two coordinate axes meet is called the
Correct Answer
D. Origin
Explanation
The point at which the two coordinate axes meet is called the origin. This is the point with coordinates (0,0) and serves as the starting point for measuring distances in the coordinate plane. It is the reference point from which all other points are located and is essential in understanding the position and direction of objects in a coordinate system.
10.
What is the coordinate of the given point?
Correct Answer
B. (4,1)
Explanation
The coordinate of the given point is (4,1) because it is the only option that matches the given answer. The first number in the coordinate represents the x-coordinate, which is the horizontal position on a graph, and the second number represents the y-coordinate, which is the vertical position on a graph. Therefore, (4,1) means that the point is located 4 units to the right and 1 unit down from the origin.