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प्रश्न
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.
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उत्तर
- (3, 0) and (-1, 0) lies on X-axis, so these are invariant under reflection on the X-axis. Hence, L1 lies on X-axis So, equation of line L1, is y = 0.
(0, -3) and (0, 1) lies on Y-axis, so these are invariant under reflection on the Y-axis. So, equation of line L2 is y = 0. - P' ⇒ (3, -4)
Q' ⇒ (-5, 2). - P'' ⇒ (-3, 4)
Q'' ⇒ (5, -2).
संबंधित प्रश्न
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”.
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.
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”.
The point P (5, 3) was reflected in the origin to get the image P’.
- Write down the co-ordinates of P’.
- If M is the foot of the perpendicular from P to the x-axis, find the co-ordinates of M.
- If N is the foot of the perpendicular from P’ to the x-axis, find the co-ordinates of N.
- Name the figure PMP’N.
- Find the area of the figure PMP’N.
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".
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.
Use graph paper for this question.
(Take 2 cm = 1 unit along both x-axis and y-axis.)
Plot the points O(0, 0), A(–4, 4), B(–3, 0) and C(0, –3).
- Reflect points A and B on the y-axis and name them A' and B' respectively. Write down their co-ordinates.
- Name the figure OABCB'A'.
- State the line of symmetry of this figure.
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.
