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Question 1: Find the coordinates of the point which lies on both x and y axes.
Solution: The only point lying on both axes is the origin. Coordinates: (0, 0).
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Question 2: Plot the points A (2, 0), B (2, 2), C (0, 2) and join OA, AB, BC and CO. What figure do you obtain?
Solution: OA = 2 units, OC = 2 units. Since it's a rectangle with adjacent sides equal, the figure is a Square.
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Question 3: Find the mirror image of the point (-3, 4) in the x-axis.
Solution: For reflection in x-axis, the sign of y-coordinate changes. Image is (-3, -4).
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Question 4: Find the area of the triangle formed by the points A(2, 0), B(6, 0) and C(4, 6).
Solution: Base AB is on x-axis. Length AB = 6 - 2 = 4 units. Height is the y-coordinate of C = 6 units.
Area = $\frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 4 \times 6 = 12$ sq units. -
Question 5: If the coordinates of two points are P(-2, 3) and Q(-3, 5), then find (abscissa of P) - (abscissa of Q).
Solution: Abscissa of P = -2. Abscissa of Q = -3.
Value = (-2) - (-3) = -2 + 3 = 1. -
Question 6: Point (0, -7) lies on which axis?
Solution: Since the x-coordinate is 0, the point lies on the y-axis (negative direction).
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Question 7: What is the perpendicular distance of the point (-4, -5) from the x-axis?
Solution: Distance is always positive. Distance from x-axis is $|y| = |-5| = 5$ units.
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Question 8: If the coordinates of a point are (-5, 11), find its mirror image in the y-axis.
Solution: For reflection in y-axis, the sign of x-coordinate changes. Image is (5, 11).
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Question 9: Plot the points P(1, 0), Q(4, 0) and S(1, 3). Find the coordinates of the point R such that PQRS is a square.
Solution: PQ is on x-axis, length = 3 units. PS is vertical, length = 3 units. To form a square, R must be (4, 3).
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Question 10: A point lies on the x-axis at a distance of 7 units from the y-axis. What are its coordinates?
Solution: Since it is on x-axis, y = 0. Distance from y-axis is 7, so x can be 7 or -7.
Coordinates are (7, 0) or (-7, 0).