Invariant Points

The point (–2, 0) on reflection in a line is mapped to (2, 0) and the point (5, –6) on reflection in the same line is mapped to (–5, –6).

1. State the name of the mirror line and write its equation.
2. State the co-ordinates of the image of (–8, –5) in the mirror line.

The points P (4, 1) and Q (–2, 4) are reflected in line y = 3. Find the co-ordinates of P’, the image of P and Q’, the image of Q.

Points (3, 0) and (−1, 0) are invarient points under reflection in the line L₁; point (0, −3) and (0, 1) are invarient points on reflection in line L₂.

1. Write the equation of the line L₁ and L₂.
2. Write down the images of points P(3, 4) and Q(−5, −2) on reflection in L₁. Name the images as P' and Q' respectively.
3. Write down the images of P and Q on reflection in L₂. Name the image as P'' and Q'' respectively.

The point P (3, 4) is reflected to P’ in the x-axis; and O’ is the image of O (the origin) when reflected in the line PP’. Write:

1. the co-ordinates of P’ and O’.
2. the length of the segments PP’ and OO’.
3. the perimeter of the quadrilateral POP’O’.
4. the geometrical name of the figure POP’O’.

Using a graph paper, plot the point A (6, 4) and B (0, 4).

(a) Reflect A and B in the origin to get the image A’ and B’.

(b) Write the co-ordinates of A’ and B’.

(c) Sate the geometrical name for the figure ABA’B’.

(d) Find its perimeter.

A’ and B’ are images of A (-3, 5) and B (-5, 3) respectively on reflection in y-axis. Find: (

a) the co-ordinates of A’ and B’.

(b) Assign special name of quadrilateral AA’B’B.

(c) Are AB’ and BA’ equal in length?

The triangle ABC, where A is (2, 6), B is (–3, 5) and C is (4, 7), is reflected in the y-axis to triangle A'B'C'. Triangle A'B'C' is then reflected in the origin to triangle A"B"C".

1. Write down the co-ordinates of A", B" and C".
2. Write down a single transformation that maps triangle ABC onto triangle A"B"C".

Use a graph paper for this question.

(Take 2 cm = 1 unit on both x and y axes)

1. Plot the following points: A(0, 4), B(2, 3), C(1, 1) and D(2, 0).
2. Reflect points B, C, D on the y-axis and write down their coordinates. Name the images as B', C', D' respectively.
3. Join the points A, B, C, D, D', C', B' and A in order, so as to form a closed figure. Write down the equation to the line about which if this closed figure obtained is folded, the two parts of the figure exactly coincide.