Coordinate Geometry
Section A: Multiple Choice Questions
1. The name of horizontal line in the cartesian plane which determines the position of a point is called:
Solution The horizontal reference line is the X-axis.
2. The name of vertical line in the cartesian plane which determines the position of a point is called:
Solution The vertical reference line is the Y-axis.
3. The section formed by horizontal and vertical lines determining the position of point in a cartesian plane is called:
Solution The axes divide the plane into four parts called Quadrants.
4. The point of intersection of horizontal and vertical lines determining the position of point in a cartesian plane is called:
Solution The point where the axes intersect is the Origin (0,0).
5. If x coordinate of a point is zero, then the point lies on:
Solution Any point with x-coordinate zero (0, y) lies on the Y-axis.
6. If the coordinates of a point are (3, 0), then it lies in:
Solution Since the y-coordinate is 0, the point lies on the X-axis.
7. Abscissa of a point is positive in:
Solution The abscissa (x-value) is positive to the right of the Y-axis, which covers Quadrants I and IV.
8. If x < 0 and y > 0, then the point lies in:
Solution Negative x and Positive y corresponds to the II Quadrant.
9. The point whose ordinate is 8 and lies on y-axis is:
Solution Points on the y-axis have x=0. Since ordinate (y) is 8, the point is (0, 8).
10. If the coordinates of a point are (0, -4), then it lies in:
Solution The x-coordinate is 0, so the point lies on the Y-axis.
Section B: Assertion-Reason Questions
Directions:
(a) Both A and R are true and R is correct explanation of A.
(b) Both A and R are true but R is not correct explanation of A.
(c) A is true but R is false.
(d) A is false but R is true.
(a) Both A and R are true and R is correct explanation of A.
(b) Both A and R are true but R is not correct explanation of A.
(c) A is true but R is false.
(d) A is false but R is true.
11. Assertion (A): A point whose abscissa is -8 and ordinate is 5 lies in second Quadrant.
Reason (R): Points of the type (-, +) lie in the second quadrant.
Reason (R): Points of the type (-, +) lie in the second quadrant.
Solution Point (-8, 5) has negative x and positive y, which is indeed the II quadrant. Reason correctly explains the sign convention.
12. Assertion (A): If the ordinate of a point is equal to its abscissa, then the point lies either in the first quadrant or in the second quadrant.
Reason (R): A point both of whose coordinates are negative will lie in the third quadrants.
Reason (R): A point both of whose coordinates are negative will lie in the third quadrants.
Solution If ordinate = abscissa (y = x), the signs must be same. This happens in Quadrant I (+,+) and Quadrant III (-,-). Assertion claims II quadrant (where signs differ), so Assertion is False. Reason is True.
13. Assertion (A): A point whose abscissa is 0 and ordinate is 2 lies on y-axis.
Reason (R): Equation of y-axis is x = 0.
Reason (R): Equation of y-axis is x = 0.
Solution Point (0, 2) has x=0, so it lies on the Y-axis. The reason correctly states that x=0 is the defining property of the y-axis.
14. Assertion (A): The perpendicular distance of the point A(3, 4) from the y-axis is 4.
Reason (R): The perpendicular distance of a point from y-axis is called its x-coordinate.
Reason (R): The perpendicular distance of a point from y-axis is called its x-coordinate.
Solution The distance from the y-axis is the absolute value of the x-coordinate. For (3,4), distance is 3. Assertion says 4, so it is False. Reason is True.
15. Assertion (A): The abscissa of point (3,5) is 5.
Reason (R): The signs of points in quadrants I, II, III and IV are respectively (+, +) ,(-, +) ,(-, -) and (+, -).
Reason (R): The signs of points in quadrants I, II, III and IV are respectively (+, +) ,(-, +) ,(-, -) and (+, -).
Solution Abscissa is the x-coordinate, which is 3. Assertion claims it is 5 (which is the ordinate). So Assertion is False. Reason is True.
16. Assertion (A): Point (2, -3) lies in IInd Quadrant.
Reason (R): A point is of the form (+, -) lies in IV Quadrant.
Reason (R): A point is of the form (+, -) lies in IV Quadrant.
Solution Point (2, -3) has positive x and negative y, so it is in the IV Quadrant. Assertion says II, so it is False. Reason is True.
17. Assertion (A): Intersection of horizontal line and vertical line is called origin.
Reason (R): coordinate of the origin is (0, 0).
Reason (R): coordinate of the origin is (0, 0).
Solution Both statements are factually true. However, stating the coordinates (Reason) doesn't explain *why* the intersection is called the "origin" (definition). Thus, (b) is the standard answer.
18. Assertion (A): The perpendicular distance of a point(-2, -5) on the axis is -5.
Reason (R): For any point, the perpendicular distance from y axis is known as abscissa.
Reason (R): For any point, the perpendicular distance from y axis is known as abscissa.
Solution Distance is a magnitude and cannot be negative. The distance is |-2| or |-5| depending on the axis, but never negative. Assertion is False. Reason is True (technically magnitude of abscissa).
19. Assertion (A): For plotting any point on the Cartesian plane, the order of a point is (x, y).
Reason (R): For a point (x, y), x coordinate is known as abscissa and y coordinate is known as ordinate.
Reason (R): For a point (x, y), x coordinate is known as abscissa and y coordinate is known as ordinate.
Solution Both are true definitions. The Reason defines the components but doesn't necessarily explain the *order* convention itself. So (b) is appropriate.
20. Assertion (A): A point (-2, -5) lies in IIIrd Quadrant.
Reason (R): Any point is of the form (-, -) lies in the IIIrd Quadrant.
Reason (R): Any point is of the form (-, -) lies in the IIIrd Quadrant.
Solution The point has both negative coordinates. The Reason states that such points lie in the III Quadrant, which explains why the Assertion is true.