Moderate Level Worksheet
Very Short Answer Questions (1 Mark Each)
(1) Write the coordinates of the point lying on the y-axis at a distance of 7 units below the origin.
Perfect! On y-axis, x = 0, and below origin means negative y-coordinate.
(2) In which quadrant does the point (5, -6) lie?
Excellent! x > 0 and y < 0, so it's in the fourth quadrant.
(3) Write the coordinates of the point lying on the x-axis at a distance of 4 units to the left of the origin.
Correct! On x-axis, y = 0, and left of origin means negative x-coordinate.
(4) Name the quadrant of the point (-8, 9).
Great! x < 0 and y > 0, so it's in the second quadrant.
(5) Write the coordinates of a point whose abscissa is 0 and ordinate is -3.
Perfect! Abscissa is x-coordinate, ordinate is y-coordinate.
Short Answer Questions (2 Marks Each)
Note: Answer each question with steps and explanation in 2-3 sentences. Write down the answers on sheet and submit to the school subject teacher.
(1) Write the coordinates of the points where the graph of y = 0 intersects the x-axis from -4 to 4.
When y = 0, all points lie on the
Points from x = -4 to x = 4:
Excellent! The equation y = 0 represents the entire x-axis.
(2) Determine the quadrants of the following points: (-2, -3), (3, -4), (-5, 6), (4, 5).
(-2, -3):
(3, -4):
(-5, 6):
(4, 5):
Perfect! You've correctly identified all quadrants.
(3) Find the coordinates of a point which is equidistant from A(0, 5) and B(0, -3) and lies on the y-axis. Required point:
Great! The midpoint is equidistant from both points.
(4) The coordinates of point P are (x, 5). If P lies on the y-axis, find the value of x. x =
Correct! Points on y-axis have x = 0.
(5) Write the coordinates of a point that is 6 units to the right of the origin and 4 units above the x-axis. Required coordinates:
Excellent! Right means positive x, above means positive y.
Long Answer Questions (4 Marks Each)
Note: Answer each question with steps and explanation. Write down the answers on sheet and submit to the school subject teacher.
(1) Plot the points A(2, 3), B(2, -3), C(-2, -3), and D(-2, 3) on the Cartesian plane. Join them in order and identify the figure.
Point A(2, 3): Quadrant
Point B(2, -3): Quadrant
Point C(-2, -3): Quadrant
Point D(-2, 3): Quadrant
Side AB: Length =
Side BC: Length =
Figure formed:
Perfect! The figure is a rectangle with length 6 and width 4.
(2) On a graph paper, plot the points P(0, 0), Q(0, 6), R(8, 6), and S(8, 0). Name the quadrilateral formed and find its perimeter.
Point P:
Point Q: On
Point R: In
Point S: On
Side PQ:
Side QR:
Side RS:
Side SP:
Quadrilateral:
Perimeter:
Excellent! It's a rectangle with perimeter 28 units.
(3) Plot the points A(-4, 2), B(-4, -2), C(4, -2), and D(4, 2). Join them and name the figure formed.
Length AB: =
Length BC: =
Length CD: =
Length DA: =
Figure formed:
Great! The opposite sides are equal, forming a rectangle.
(4) Plot the points M(0, -5), N(5, 0), O(0, 5), and P(-5, 0). Join them in order and describe the figure.
Point M: On
Point N: On
Point O: On
Point P: On
All sides equal: Each =
Figure formed:
Perfect! It's a square rotated 45° with vertices on the axes.
(5) Plot and name the quadrilateral formed by A(-3, 4), B(-3, -4), C(3, -4), and D(3, 4). Find the lengths of its sides.
Side AB: =
Side BC: =
Side CD: =
Side DA: =
Quadrilateral:
Excellent! It's a rectangle with sides 8 and 6 units.
Part B: Objective Questions (1 Mark Each)
Choose the correct answer and write the option (a/b/c/d)
(1) The point (-4, 0) lies:
(a) In the first quadrant (b) In the second quadrant (c) On the x-axis (d) On the y-axis
Correct! Since y = 0, the point lies on the x-axis.
(2) The point (0, -7) lies:
(a) On the x-axis (b) On the y-axis (c) In the third quadrant (d) In the fourth quadrant
Correct! Since x = 0, the point lies on the y-axis.
(3) A point whose abscissa is zero lies:
(a) On the x-axis (b) On the y-axis (c) In the first quadrant (d) In the second quadrant
Correct! Abscissa is x-coordinate; when x = 0, point lies on y-axis.
(4) The point (-5, -2) lies in the:
(a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
Correct! Both coordinates are negative, so it's in the third quadrant.
(5) The coordinates of a point lying 4 units to the left of the origin on the x-axis are:
(a) (-4, 0) (b) (0, -4) (c) (4, 0) (d) (0, 4)
Correct! Left means negative x, and on x-axis means y = 0.
(6) Which of the following points lies in the first quadrant?
(a) (3, -2) (b) (-3, -2) (c) (3, 2) (d) (-3, 2)
Correct! First quadrant has x > 0 and y > 0.
(7) The coordinates of a point in the second quadrant are:
(a) x > 0, y > 0 (b) x < 0, y > 0 (c) x > 0, y < 0 (d) x < 0, y < 0
Correct! Second quadrant has negative x and positive y.
(8) Which of the following points lies in the fourth quadrant?
(a) (-4, 5) (b) (4, -5) (c) (-4, -5) (d) (4, 5)
Correct! Fourth quadrant has positive x and negative y.
(9) The coordinates (0, 0) represent:
(a) Origin (b) Centre (c) Intersection point of axes (d) Both a and c
Correct! (0,0) is both the origin and the intersection of axes.
(10) The point (x, 0) lies on the:
(a) x-axis (b) y-axis (c) First quadrant (d) Second quadrant
Correct! When y = 0, the point lies on the x-axis.
Excellent! You understand the distinction between axis points and quadrant points.
True or False: Advanced Coordinate Properties
Determine whether these statements are True or False: