Question

Use graph paper to answer the following questions. (Take 2 cm = 1 unit)

1. Plot the points A(– 4, 2) and B(2, 4). 
2. A' is the image of A when reflected in the y-axis. Plot it on the graph paper and write the co-ordinates of A'. 
3. B' is the image of B when reflected in the line AA'. Write the co-ordinates of B'. 
4. Write the geometric name of the figure ABA'B'. 
5. Name a line of symmetry of the figure formed. 

Answer 1

Here’s the graph (1 big square = 1 unit, i.e. 2 cm):

i. A(– 4, 2) and B(2, 4) are plotted on the graph above, with 1 unit = 2 cm.

ii. Reflection in the y-axis maps (x, y) to (–x, y), so A′ is (4, 2).

iii. AA′ is the line y = 2. B(2, 4) is 2 units above this line, so its image is 2 units below it. B′ is (2, 0).

iv. ABA′B′ is a kite. It has two pairs of equal adjacent sides:

AB = AB′

= `sqrt(6^2 + 2^2)` 

= `sqrt(40)` units

BA′ = B′A′

= `sqrt(2^2 + 2^2)` 

= `sqrt(8)` units

v. The line AA′ (y = 2) is a line of symmetry of the kite.