Important MCQs on Coordinate Geometry with Explanation

Ans. (d) I and IV quadrant

Explanation: The x-coordinate of a point on the coordinate plane is referred to as abscissa. An ordered pair of numbers is referred to as the coordinates where the first number is the abscissa i.e. the measurement along the X-axis. The signs of the coordinates are 

• The first quadrant is (+, +)
• The second quadrant is (−, +)
• The third quadrant is (−, −)
• The fourth quadrant is (+, −)

Hence, the abscissa of a point is positive in the I and IV quadrant.

Ans. (b) x-axis

Explanation: The horizontal line drawn to determine the position of any point in a Cartesian plane is referred to as the x-axis. On the other hand, the vertical line drawn to determine the position of any point in the Cartesian plane is referred to as the y-axis.

Read More: X and Y Intercepts, Form, Graph and Formula

Ans. (c) II and IV quadrants respectively.

Explanation: On comparing the given points with the (x,y) coordinates, we will see that

Point (-5,2) is of the form (-x,y) thus, it lies in the II quadrant.

Point (2,-5) is of the form (x,-y) thus, it lies in the IV quadrant.

Therefore, the points (-5,2) and (2,-5) lies in the II and IV quadrant respectively.

Ans. (a) (3,6)

Explanation: From the question, we are given:

(x+2, 4) = (5, y-2)

On equating both the abscissa and the ordinate we will obtain,

From R.H.S, x + 2 = 5

x = 5-2

x = 3

From L.H.S, y – 2 = 4

y = 4 +2

y = 6

Therefore the coordinates of (x,y) = (3,6).

Ans. (d) (-9,-8)

Explanation: A mirror image is a point whose distance is the same from the origin O (0,0) and the same from both the axes as of the point (9,-8) is. From the question, we can conclude that the point (9,-8) lies in the IV quadrant,

Since the given point lies in the IV quadrant, its mirror image in accordance with the y-axis must lie in the III quadrant where the x-coordinate of any point (x,y) is negative.

Hence, the mirror image of the given point (9,-8) will be formed at coordinate (-9,-8).

Read More: Abscissa, Plotting Ordinates, Relation, Solved Examples

Ans. (d) (0,-4)

Explanation: Since the point lies on the y-axis in the negative direction it implies that the point is either in the III quadrant or in the IV quadrant as only in these quadrant does the y-axis has negative coordinates. Therefore, the coordinates of the point which lies on the y-axis are (0,-4)

Ans. (b) 3

Explanation: Since the points lie on the x-axis this implies that the y-axis will be 0. Using this concept, the value of a can be determined.

As the point R (3, a-3) lies on the x-axis, therefore y-axis must be 0. From the given point we can take the y-coordinate as a-3. Hence,

a - 3 = 0

a = 3

Thus the value of a will be 3.

Ans. (a) (-4,0)

Explanation: For a point to lie on the negative side of the x-axis, the point must be on the left side of the XY plane. From the given options in the question, only the point (-4,0) lies on the negative side of the x-axis.

Ans. (b) (-3,-3.5)

Explanation: From the image given in the question, it can be noticed that point Q lies in the III quadrant. In the III quadrant, the coordinates are (-x,-y) i.e. both the x and y points are negative. Hence the coordinates of point Q will be (-3, -3.5).

Ans. (d) (a,-b)

Explanation: In the question, point M lies in the IV quadrant. As in the IV quadrant, only the x coordinate is positive and the y-coordinate is negative. Therefore, the point M in the IV quadrant will have coordinates (a,-b) where x = a, and y = -b.

Read More: Ordered Pairs

Ans. III quadrant

Explanation: Since, in the III quadrant only, both the coordinates of the x-axis and y-axis are negative hence the point (-3,-5) will lie in the III quadrant of the XY plane.

Ans. (b) 0

Explanation: Abscissa refers to the x-coordinate of a point in a 2D Cartesian coordinate system. On the y axis, the value of the x-coordinate is 0 Hence, Abscissa of any point on the y axis will be 0.

Ans. (c) 8

Explanation: From the given diagram we can determine the value of side CD i.e. 6 - 2 = 4.

Length AB = length DC

At line AB,

y = 4, so y coordinate of B = 4

Distance CD = 6 – 2

=> 4

x-coordinate of B = 4 + 4

=> 8

Therefore, the coordinate of point B (8,5).

Read More: Parallelogram

Ans. (d) Quadrants

Explanation: The horizontal and vertical lines drawn for determining the position of any point in the Cartesian plane is referred to as the x-axis and y-axis respectively. The name of sections of the plane which are formed by the two-lines x-axis and y-axis is referred to as quadrants.

Ans. (d) Don’t lie in the same quadrant

Explanation: The first point Q has coordinates (1,2) which lies in the I quadrant as both the x and y coordinates are positive. The second point R has coordinates (-2,-3) which lies in the III quadrant as both the x and y coordinates are negative. The last point S has coordinates (2,-3) which lies in the IV quadrant as the x coordinate is positive and the y coordinate is negative.

Since all the given points are different quadrants thus it can be concluded that option (d) is the right answer.

Ans. (d) y-axis

Read More: Introduction to Three-Dimensional Geometry

Explanation: Since the x coordinate of a point is 0 then it implies that the point is on the y-axis because only at the y-axis, the x coordinate is 0.

Ans. (c) 0

Explanation: An ordinate refers to the y-coordinate of a point in a 2D Cartesian coordinate system. For all points on the x-axis, the ordinate is 0. Since, the coordinates of any point on the x-axis is (x, 0). In this situation, the abscissa can take any value and the ordinate is 0.

Read More: Different Forms of the Equation of Line

Ans. (d) Any number

Explanation: For any point on the x-axis, the coordinate is (x,0) where x can take any value. Hence, the abscissa of all the points can be any number of the x-axis.

Ans. (a) Y-coordinate = 7 or -7 only

Explanation: The perpendicular distance of any point from the x-axis gives the y-coordinate of that point. According to the question, the foot of the perpendicular lies in the negative direction of the x-axis therefore the perpendicular distance can be measured in II or III quadrants. Thus, we can conclude that the point P will have coordinate = 7 or -7.

Ans. (d) -1

Explanation: Abscissa refers to the x-coordinate of the point thus,

Abscissa of point P = -7

Abscissa of point Q = -6

(abscissa of P) – (abscissa of Q)

= (-7) – (-6)

= -7 + 6

=> -1