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प्रश्न
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.
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उत्तर
A point P (a, b) is reflected in the x-axis to P’ (2, –3).
We know Mx (x, y) = (x, –y)
Thus, co-ordinates of P are (2, 3).
Hence, a = 2 and b = 3.
P” = Image of P reflected in the y-axis = (–2, 3)
P”’ = Reflection of P in the line (x = 4) = (6, 3)
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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”.
- Point P (a, b) is reflected in the x-axis to P’ (5, –2). Write down the values of a and b.
- P” is the image of P when reflected in the y-axis. Write down the co-ordinates of P”.
- Name a single transformation that maps P’ to 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.
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.
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.
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:
- the co-ordinates of P’ and O’.
- the length of the segments PP’ and OO’.
- the perimeter of the quadrilateral POP’O’.
- 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".
- Write down the co-ordinates of A", B" and C".
- Write down a single transformation that maps triangle ABC onto triangle A"B"C".
- 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.
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.
