Question

The image of triangle OXY under reflection in the origin, O is the triangle OX₁Y₁, where X₁(-3, -4) is the image of X and Y₁, (0, -5) is the image of Y.
(i) Draw a diagram to represent this information and write down the co-ordinates of X and Y.
(ii) What kind of figure is the quadrilateral XYX₁Y₁? Give reason for your answer. State, with a reason, whether the figure XYX₁Y₁ has any lines of symmetry.
(iii) Find the co-ordinates of X₂, the image of X under reflection in the origin followed by reflection on the Y-axis.
(iv) Find the co-ordinates of Y₂, the image of Y under reflection on the X-axis followed by reflection in the origin.

Answer 1

(i)
X₁ → (-3, -4)
X → (3, 4)
Y₁ → (0, -5)
Y → (0, 5).

(ii) Rectangle.
Reasons : X₁Y₁ = YX
and  X₁Y₁ = Y₁X
Also each angle of the quadrilateral XYX₁Y₁ is 90°.
It has two lines of symmetry. These are the perpendicular bisectors of each pair of opposite sides.
(iii) X₂ = (3, -4).
(iv) Y₂ = (0, 5).