Question

1. Draw rectangular axes. Scale them from
0 to 18. Plot the points : A (3, 4), B (9,4), C (9,6),
D (3,6). Join the points in alphabetical order to
form a rectangle. Transform each of the points
(x, y) on the points (x, y) by the transformation
(x,y) → (2.x, 2y)
Label image A,B,C,D, to correspond with
ABCD.
(i) What do you notice about the length of
each side of the image when you compare it
with the corresponding side of the original
rectangle?
(ii) Are the rectangles similar in shape?
Area of image A;B,C,D
(iii) Write the ratio
in
Area of original ABCD
the lowest terms.

​

Answer 1

1. Step-by-step explanation:

Draw the x and y axes. Mark the units along the x and y axes with a suitable scale.

(i) To plot the point A (3 , 5) 

      Here, the x-coordinate of A is 3 and the y-coordinate of A is 5. Both are positive. Hence the point A (3 , 5) lies in the  quadrant I. Start at the Origin. Move three units to the right along the x-axis. Then turn and move 5 units up parallel to Y-axis and mark the point A (3 , 5). 

(ii) To plot the point B (2 , 7) 

     Here, the x-coordinate of B is -2 which is negative and the y-coordinate of B is 7 which is positive. Hence the point  B (-2 , 7) lies in the quadrant II. Start at the Origin. Move 2 units to the left along the x-axis. Then  turn and move 7 units up parallel to y-axis and mark the point B (-2 , 7). 

(iii) To plot the point C (-3 , -5) Here, the x-coordinate of C is -3 and the y-coordinate of C is -5. Both are negative. Hence the point C (-3 , -5) lies in the quadrant III. Start at the Origin. Move 3 units to the left along the x-axis. Then turn and move 5 units down parallel to y-axis. and mark the point C (-3, -5). 

(iv) To plot the point D (2 , 7) 

      Here, the  x-coordinate of the point D is 2 which is positive and the y-coordinate of D is -7 which is negative. Hence the point D (2 , -7) lies in the quadrant IV. Start at the Origin. Move 2 units to the right along the x-axis. Then turn and move 7 units down parallel to y-axis and mark the point D (2 , -7). 

(v) To plot the point O (0, 0) 

      This is the origin. Both the x and y coordinates are zeros. It is the point of  intersection of the axes x and y. Mark the point O (0,0).