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Question
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).
- State the name of the mirror line and write its equation.
- State the co-ordinates of the image of (–8, –5) in the mirror line.
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Solution
i. We know reflection of a point (x, y) in y-axis is (–x, y).
Hence, the point (–2, 0) when reflected in y-axis is mapped to (2, 0).
Thus, the mirror line is the y-axis and its equation is x = 0.
ii. Co-ordinates of the image of (–8, –5) in the mirror line (i.e., y-axis) are (8, –5).
RELATED QUESTIONS
Attempt this question on graph paper.
- Plot A (3, 2) and B (5, 4) on graph paper. Take 2 cm = 1 unit on both the axes.
- Reflect A and B in the x-axis to A’ and B’ respectively. Plot these points also on the same graph paper.
- Write down:
- the geometrical name of the figure ABB’A’;
- the measure of angle ABB’;
- the image of A” of A, when A is reflected in the origin.
- the single transformation that maps A’ to A”.
Points (3, 0) and (–1, 0) are invariant points under reflection in the line L1; points (0, –3) and (0, 1) are invariant points on reflection in line L2.
- Name or write equations for the lines L1 and L2.
- Write down the images of the points P (3, 4) and Q (–5, –2) on reflection in line L1. Name the images as P’ and Q’ respectively.
- Write down the images of P and Q on reflection in L2. Name the images as P” and Q” respectively.
- State or describe a single transformation that maps P’ onto P''.
Points A and B have co-ordinates (3, 4) and (0, 2) respectively. Find the image:
- A’ of A under reflection in the x-axis.
- B’ of B under reflection in the line AA’.
- A” of A under reflection in the y-axis.
- B” of B under reflection in the line AA”.
- Plot the points A (3, 5) and B (–2, –4). Use 1 cm = 1 unit on both the axes.
- A’ is the image of A when reflected in the x-axis. Write down the co-ordinates of A’ and plot it on the graph paper.
- B’ is the image of B when reflected in the y-axis, followed by reflection in the origin. Write down the co-ordinates of B’ and plot it on the graph paper.
- Write down the geometrical name of the figure AA’BB’.
- Name the invariant points under reflection in the x-axis.
A (1, 1), B (5, 1), C (4, 2) and D (2, 2) are vertices of a quadrilateral. Name the quadrilateral ABCD. A, B, C, and D are reflected in the origin on to A’, B’, C’ and D’ respectively. Locate A’, B’, C’ and D’ on the graph sheet and write their co-ordinates. Are D, A, A’ and D’ collinear?
P and Q have co-ordinates (0, 5) and (–2, 4).
- P is invariant when reflected in an axis. Name the axis.
- Find the image of Q on reflection in the axis found in (a).
- (0, k) on reflection in the origin is invariant. Write the value of k.
- Write the co-ordinates of the image of Q, obtained by reflecting it in the origin followed by reflection in x-axis.
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".
- Write down the co-ordinates of A", B" and C".
- Write down a single transformation that maps triangle ABC onto triangle A"B"C".
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?
Use a graph paper for this question.
(Take 2 cm = 1 unit on both x and y axes)
- Plot the following points: A(0, 4), B(2, 3), C(1, 1) and D(2, 0).
- Reflect points B, C, D on the y-axis and write down their coordinates. Name the images as B', C', D' respectively.
- 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.
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.
- Write the equation of the line L1 and L2.
- 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.
- Write down the images of P and Q on reflection in L2. Name the image as P'' and Q'' respectively.
