Points `P` and `Q`, shown on the Cartesian plane diagram, are rotated 180° about the origin and become points `P^(′)` and `Q^(′)`.
Plot the points `P^(′)` and `Q^(′)` on the diagram. (3 marks)
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Points `P` and `Q`, shown on the Cartesian plane diagram, are rotated 180° about the origin and become points `P^(′)` and `Q^(′)`.
Plot the points `P^(′)` and `Q^(′)` on the diagram. (3 marks)
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`P^(′)(2,1)`
`Q^(′)(-4,2)`
Point `Q(3,1)` on the Cartesian plane is rotated 180° about the origin in a clockwise direction to become point `Q^(′)`.
What are the coordinates of `Q^(′)`. (2 marks)
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`Q^(′)(-3,-1)`
Gabby put 5 points on a grid and labelled them `A` to `E`, as shown on the diagram below.
Point `A` is 35 millimetres from point `D.`
Gabby adds a sixth point, `F` so that the arrangement of points has one line of symmetry.
How far is point `F` from point `B?` (3 marks)
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`42\ text{mm}`
The trapezium `ABCD` is moved to the new position shown by trapezium `SRQP.`
Which of these transformations resulted in the new position?
`C`
`text(Reflection in the)\ xtext(-axis:)`
`ABCD -> A^{prime}B^{prime}C^{prime}D^{prime}`
`text(Translate 8 units left:)`
`A^{prime}B^{prime}C^{prime}D^{prime} -> SRQP`
`=>C`
Rochelle drew a pattern which is pictured below.
Rochelle rotates the pattern.
How much does Rochelle to turn the pattern until it looks exactly the same?
`B`
`text(Outer pattern looks the same every)\ \ 1/8\ \ text(turn).`
`text(Inner cross pattern looks the same every)\ \ 1/4\ \ text(turn).`
`:.\ text(Whole pattern looks the same every)\ \ 1/4\ \ text(turn).`
`=>B`
This shape will be translated 4 units to the right and 2 units up.
Where will the image of the point `A` be located after the shape is translated? (2 marks)
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`(1,−3)`
`text(Current position)\ A(−3,−5)`
`text(Translate 4 units to right:)`
`A(−3 + 4,−5) \ -> \ (1,−5)`
`text(Translate 2 units up:)`
`(1,−5+2 ) \ -> \ (1,−3)`
`:. text(Image of)\ A\ text(is)\ (1,−3)`
The point `P(-1, -4)` lies on the Cartesian plane. It is reflected in the `x`-axis to form the point `P^(′)`.
Find the coordinates of `P^(′)`. (1 mark)
`(-1,4)`
`text(Reflections in the)\ xtext{-axis:}`
`ytext{-coordinate has opposite sign and}\ xtext{-coordinate is the same.}`
`P(-1,-4)\ ->\ P^(′)(-1,4)`
The point `P(-3, 7)` lies on the Cartesian plane. It is reflected in the `y`-axis to form the point `P^(′)`.
Find the coordinates of `P^(′)`. (1 mark)
`(7,5)`
`text(Reflections in the)\ ytext{-axis:}`
`xtext{-coordinate has opposite sign and}\ ytext{-coordinate is the same.}`
`P(-3,7)\ ->\ P^(′)(3,7)`
`P(2,3)` is translated 3 units up and 4 units left.
The new point is then reflected in `x`-axis to form point `P^(′)`.
Find the coordinates of `P^(′)`. (2 marks)
`(-2,-6)`
`text{1st transformation:}`
`(2,3)\ ->\ (2-4, 3+3)\ ->\ (-2,6)`
`text{2nd transformation (reflection):}`
`(-2,6)\ ->\ P^(′)(-2,-6)`
`P(-3,-5)` is reflected in the `x`-axis and then translated 3 units to the right to form point `P^(′)`.
Find the coordinates of `P^(′)`. (2 marks)
`(0,5)`
`text{1st transformation (reflection):}`
`P(-3,-5)\ ->\ (-3,5)`
`text{2nd transformation:}`
`(-3,5)\ ->\ (0,5)`
The point `A(-2, 5)` lies on the Cartesian plane. It is translated five units left and then reflected in the `y`-axis.
Find the coordinates of the final image of `A`. (2 marks)
`(7,5)`
`text(1st transformation:)`
`A(-2, 5)\ ->\ (-7,5)`
`text{2nd transformation (reflection):}`
`(-7,5)\ ->\ (7,5)`
The point `P(4, -3)` lies on the Cartesian plane. It is translated four units vertically up and then reflected in the `y`-axis.
Find the coordinates of the final image of `P`. (2 marks)
`(-4,1)`
`text(1st transformation:)`
`P(4,-3)\ ->\ (4,1)`
`text{2nd transformation (reflection):}`
`(4,1)\ ->\ (-4,1)`