Use graph sheet for this question. Take 2 cm = 1 unit along both x and y axis. Graphically represent parallelogram OABC, where O(0, 0), A(2, 3), B(5, 3) and C(3, 0).
Reflect OABC :
(a) on the x-axis and name its image as ODEC.
(b) through the origin and name its image as OIJH.
(c) on the y-axis and name its image as OFGH.
From graph, on reflecting O, A, B, C on x-axis we get,
O(0, 0) ⇒ O(0, 0)
A(2, 3) ⇒ D(2, -3)
B(5, 3) ⇒ E(5, -3)
C(3, 0) ⇒ C(3, 0)
(b) From graph, on reflecting O, A, B, C trough origin we get,
O(0, 0) ⇒ O(0, 0)
A(2, 3) ⇒ I(-2, -3)
B(5, 3) ⇒ J(-5, -3)
C(3, 0) ⇒ H(-3, 0)
(c) From graph, on reflecting O, A, B, C on y-axis we get,
O(0, 0) ⇒ O(0, 0)
A(2, 3) ⇒ F(-2, 3)
B(5, 3) ⇒ G(-5, 3)
C(3, 0) ⇒ H(-3, 0)
More ICSE Moderate level questions
Use graph paper, taking 2 cm = 1 unit along both axes. (a) Plot A(1, 3), B(1, 2) and C(3, 0). (b) Reflect A and B in the x-axis and name their images E and D. Write their coordinates. (c) Reflect A and B through the origin and name their images F and G. (d) Reflect A, B and C in the y-axis and name their images J, I and H. (e) Join A, B, C, D, E, F, G, H, I and J in order and name the closed figure.
Use a graph sheet for this question. (a) Plot A(0, 3), B(2, 1) and C(4, −1). (b) Reflect points B and C in the y-axis and name their images B′ and C′ respectively. Plot and write the coordinates of B′ and C′. (c) Reflect point A in the line BB′ and name its image A′. (d) Plot and write the coordinates of A′. (e) Join the points ABA′B′ and give the geometrical name of the closed figure so formed.
Use graph sheet to answer this question. Take 2 cm = 1 unit along both the axes. (a) Plot A, B and C where A(0, 4), B(1, 1) and C(4, 0). (b) Reflect A and B on the x-axis and name them E and D respectively. (c) Reflect B through the origin and name it F. Write down the coordinates of F. (d) Reflect B and C on the y-axis and name them H and G respectively. (e) Join A, B, C, D, E, F, G, H and A in order and name the closed figure formed.
The 4th and the 7th terms of an A.P. are 60 and 114 respectively. Find: (a) the first term and the common difference. (b) the sum of the first 10 terms.
Prove that: (sec θ − cos θ)(cosec θ − sin θ) = sin θ cos θ
Solve the quadratic equation (x − 2)² − 5x − 3 = 0 and give your answer correct to 3 significant figures.
In the given diagram, O is the centre of the circle and the tangent DE touches the circle at B. If ∠ADB = 32°. Find the values of x and y.
The total surface area of a sphere S₁ of radius R and the total surface area of a solid hemisphere S₂ of radius r are equal. The ratio R : r is: (a) 1 : 1 (b) 2 : 1 (c) √3 : 2 (d) 2 : √3
In the given figure, AOB is a right-angled triangle and C is the midpoint of the hypotenuse AB. If the coordinates of C are (x, y), the point equidistant from A, O and B is: (a) (x, y) (b) (y, x) (c) (x/2, y/2) (d) (2x/3, 2y/3)
Find the equation of a line whose y-intercept is 6 and is parallel to x-axis. (a) y = 6 (b) x = 6 (c) x + y = 6 (d) y − x = 6
Assertion (A): The 9th term of the G.P. 6, −12, 24, −48, … is positive. Reason (R): (−2)⁸ is positive. (a) A is true and R is false. (b) A is false and R is true. (c) Both A and R are true and R is the correct explanation of A. (d) Both A and R are true but R is not the correct explanation of A.
What must be added to x³ + 7x² + 3x + 2 so that the resulting polynomial is exactly divisible by x + 2? (a) −40 (b) −16 (c) 16 (d) 40
