मराठी

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. (I) Write the Equation of the Line L1 and L2. - Mathematics

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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.

  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.
बेरीज
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उत्तर

  1. (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.
  2. P' ⇒ (3, -4)
    Q' ⇒ (-5, 2).
  3. P'' ⇒ (-3, 4)
    Q'' ⇒ (5, -2).
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संबंधित प्रश्‍न

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.

A point P (–2, 3) is reflected in line x = 2 to point P’. Find the co-ordinates of P’.


A point P (a, b) is reflected in the x-axis to P’ (2, –3). Write down the values of a and b. P” is the image of P, reflected in the y-axis. Write down the co-ordinates of P”. Find the co-ordinates of P”’, when P is reflected in the line, parallel to y-axis, such that x = 4.


Points A and B have co-ordinates (3, 4) and (0, 2) respectively. Find the image:

  1. A’ of A under reflection in the x-axis.
  2. B’ of B under reflection in the line AA’.
  3. A” of A under reflection in the y-axis.
  4. B” of B under reflection in the line AA”.

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’.

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".

  1. The point P (2, –4) is reflected about the line x = 0 to get the image Q. Find the co-ordinates of Q.
  2. The point Q is reflected about the line y = 0 to get the image R. Find the co-ordinates of R.
  3. Name the figure PQR.
  4. Find the area of figure PQR.

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?


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 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.

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