Question

(For this question, use a graph paper. Scale: 1 cm = 1 unit along both x and y-axis.)

Plot points A(0, 3), B(4, 0), C(6, 2) and D(5, 0). Reflect the points as given below and write their coordinates:

1. Reflect A on x-axis to A’. 
2. Reflect B on y-axis to B’. 
3. Reflect C on x-axis to C’. 
4. D remain invariant when reflected on the line whose equation is ______.
5. Join the points A, B, C, D, C’, B, A’, B’ and A to form a closed figure. Name the closed figure BCDC’.

Answer 1

1. Reflected coordinates

The coordinates for the reflected points are found by changing the sign of the axis opposite to the reflection line:

a. Reflect A(0, 3) on x-axis: A’(0, –3). The y-coordinate changes sign.

b. Reflect B(4, 0) on y-axis: B’(–4, 0). The x-coordinate changes sign.

c. Reflect C(6, 2) on x-axis: C’(6, –2). The y-coordinate changes sign.

2. Invariant point

d. Point D(5, 0) remains invariant when reflected on the line whose equation is y = 0 the x-axis. This is because the point already lies on this line, so its position does not change during reflection.

3. Forming the closed figure

e. Joining the points in the order A → B → C → D → C’ → B → A’ → B’ → A creates a complex closed figure.

Name the closed figure BCDC': Based on the points B(4, 0), C(6, 2), D(5, 0), and C’(6, –2), the figure BCDC’ is a kite (specifically, a concave one or a “dart” shape) symmetric about the x-axis.

The coordinates are A’(0, –3), B’(–4, 0) and C’(6, –2). The line of invariance for D is y = 0.