हिंदी

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. - Mathematics

Advertisements
Advertisements

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.
योग
Advertisements

उत्तर

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).

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?

संबंधित प्रश्न

Attempt this question on graph paper.

  1. Plot A (3, 2) and B (5, 4) on graph paper. Take 2 cm = 1 unit on both the axes.
  2. Reflect A and B in the x-axis to A’ and B’ respectively. Plot these points also on the same graph paper.
  3. Write down:
    1. the geometrical name of the figure ABB’A’;
    2. the measure of angle ABB’;
    3. the image of A” of A, when A is reflected in the origin.
    4. the single transformation that maps A’ to A”.

  1. Point P (a, b) is reflected in the x-axis to P’ (5, –2). Write down the values of a and b.
  2. P” is the image of P when reflected in the y-axis. Write down the co-ordinates of P”.
  3. Name a single transformation that maps P’ to P”.

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.


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”.

  1. Plot the points A (3, 5) and B (–2, –4). Use 1 cm = 1 unit on both the axes.
  2. 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.
  3. 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.
  4. Write down the geometrical name of the figure AA’BB’.
  5. Name the invariant points under reflection in the x-axis.

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’.

  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.

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.

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.

Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×