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प्रश्न
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.
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उत्तर
a. Any point that remains unaltered under a given transformation is called an invariant.
It is given that P (0, 5) is invariant when reflected in an axis. Clearly, when P is reflected in the y-axis then it will remain invariant. Thus, the required axis is the y-axis.
b. The co-ordinates of the image of Q (–2, 4) when reflected in y-axis is (2, 4).
c. (0, k) on reflection in the origin is invariant. We know the reflection of origin in origin is invariant. Thus, k = 0.
d. Co-ordinates of image of Q (–2, 4) when reflected in origin = (2, –4)
Co-ordinates of image of (2, –4) when reflected in x-axis = (2, 4)
Thus, the co-ordinates of the point are (2, 4).
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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”.
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''.
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.
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 (–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:
- 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”.
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?
- The point P (2, –4) is reflected about the line x = 0 to get the image Q. Find the co-ordinates of Q.
- The point Q is reflected about the line y = 0 to get the image R. Find the co-ordinates of R.
- Name the figure PQR.
- Find the area of figure PQR.
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.
