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Question
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.
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Solution
(a)
(b) Co-ordinates of A'=(-6,-4)
Co-ordinates of B'=(0,-4)
(c) ABA'B' is parallelogram.
(d) In ABA'B',BB'=8 units, A'B'=6 units
`therefore BA'=sqrt(6^2+8^2)=sqrt(36+64)=sqrt100=10 `units
`=>B'A=10 ` units
AB=A'B'=6units
∴ the perimeter of ABA'B'=AB+BA'+A'B'+B'A
=6+10+6+10
=32 units
RELATED QUESTIONS
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''.
- 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”.
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”.
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’.
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 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.
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?
