QQuestion
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.
✓Answer
(a) Plot A(0, 4), B(1, 1) and C(4, 0) using the given scale.
(b) Reflection in the x-axis changes (x, y) to (x, −y).
Therefore, E, the reflection of A(0, 4), is E(0, −4).
D, the reflection of B(1, 1), is D(1, −1).
(c) Reflection through the origin changes (x, y) to (−x, −y).
Therefore, F, the reflection of B(1, 1), is F(−1, −1).
(d) Reflection in the y-axis changes (x, y) to (−x, y).
Therefore, H, the reflection of B(1, 1), is H(−1, 1).
G, the reflection of C(4, 0), is G(−4, 0).
(e) On joining A, B, C, D, E, F, G, H and A in order, the closed figure formed is a star.
[Completed graph space]
Related Questions
More ICSE Easy level questions
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.
What number must be added to each of the numbers 4, 6, 8 and 11 so that the resulting four numbers are in proportion?
A bag contains 25 cards numbered from 1 to 25. A card is drawn at random. Find the probability that the number on the card drawn is: (a) a multiple of 5 (b) a perfect square (c) a prime number.
The following distribution gives the daily wages of 60 workers of a factory: Daily income (₹) Number of workers 200–300 6 300–400 10 400–500 14 500–600 16 600–700 10 700–800 4 Use graph paper. Take 2 cm = ₹100 along one axis and 2 cm = 2 workers along the other axis. Draw a histogram and hence find the mode of the distribution.
Find the value of ‘a’ if x − a is a factor of the polynomial 3x3 + x2 − ax − 81.
Which of the following cannot be determined graphically for a grouped frequency distribution? (a) Median (b) Mode (c) Quartiles (d) Mean
Use graph paper to answer this question. During a medical check-up of 60 students in a school, their weights were recorded as follows: Weight (kg) Number of students 28–30 2 30–32 4 32–34 10 34–36 13 36–38 15 38–40 9 40–42 5 42–44 2 Taking 2 cm = 2 kg along one axis and 2 cm = 10 students along the other axis, draw an ogive. Use the graph to find: (a) the median (b) the upper quartile (c) the number of students whose weight is above 37 kg.
From the top of a tower 100 m high, a man observes the angles of depression of two ships A and B on opposite sides of the tower as 45° and 38° respectively. If the foot of the tower and the ships are in the same horizontal line, find the distance between ships A and B to the nearest metre. Use mathematical tables.
Using componendo and dividendo, solve for x: = 3
Using ruler and compass, construct a triangle ABC in which AB = 6 cm, ∠BAC = 120° and AC = 5 cm. Construct a circle passing through A, B and C. Measure and write down the radius of the circle.
The following table gives the marks scored by a set of students in an examination. Calculate the mean of the distribution using the shortcut method. Marks Number of students (f) 0–10 3 10–20 8 20–30 14 30–40 9 40–50 4 50–60 2
A and B are two points on the x-axis and y-axis respectively, as shown in the figure. (a) Write down the coordinates of A and B. (b) P is a point on AB such that AP : PB = 3 : 1. Using the section formula, find the coordinates of P. (c) Find the equation of a line passing through P and perpendicular to AB.