TransformationsIB MYP Maths Standard: Subtopic test

1. 1
   Triangle $T$ has vertices $A(1,1)$, $B(4,1)$ and $C(4,3)$ on a coordinate grid.

   (a)

   $T$ is reflected in the line $x=5$. Which point is the image of $A$?

   [1 mark]

   • A$(-1,1)$
   • B$(9,1)$
   • C$(6,1)$
   • D$(1,9)$

   (b)

   $T$ is reflected in the line $y=x$. Which point is the image of $C$?

   [1 mark]

   • A$(4,-3)$
   • B$(-4,3)$
   • C$(-3,-4)$
   • D$(3,4)$

   (c)

   $T$ is reflected in the $x$-axis to give triangle $T_1$. Find the coordinates of the vertices of $T_1$.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   The point $M(3,2)$ is plotted on a coordinate grid. The origin is $O$.

   (a)

   $M$ is rotated $90^\circ$ anticlockwise about $O$. Which point is the image of $M$?

   [1 mark]

   • A$(-2,3)$
   • B$(2,-3)$
   • C$(-3,-2)$
   • D$(3,-2)$

   (b)

   Which single transformation maps $M$ onto the point $(2,-3)$?

   [1 mark]

   • AReflection in the $x$-axis
   • BRotation of $90^\circ$ anticlockwise about $O$
   • CRotation of $90^\circ$ clockwise about $O$
   • DReflection in the line $y=x$

   (c)

   $M$ is rotated $180^\circ$ about the point $(1,1)$. Find the coordinates of the image of $M$.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   Triangle $A$ has vertices $(1,1)$, $(3,1)$ and $(3,2)$ on a coordinate grid.

   (a)

   Triangle $B$ is the image of $A$ after an enlargement with scale factor $3$ and centre $(0,0)$. Find the coordinates of the vertices of $B$.

   [3 marks]

   (b)

   Triangle $C$ is the image of $A$ after an enlargement with scale factor $2$ and centre $(1,1)$. Find the coordinates of the vertices of $C$.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A game designer moves a character on a coordinate grid. A character at the point $P(a,b)$ is reflected in the line $y=x$, and the image is then reflected in the $x$-axis to give the final position $P''$.

   (a)

   (i) Find $P''$ when $P$ is $(2,5)$.
   (ii) Find $P''$ when $P$ is $(6,-1)$.
   (iii) Describe the pattern, and write a rule for the coordinates of $P''$ in terms of $a$ and $b$.
   (iv) Verify your rule using the point $(-3,4)$.

   [6 marks]

   (b)

   The designer wants a single transformation that does the same job as the two reflections. Describe fully the single transformation that maps $P$ onto $P''$. Justify your answer using the point $(2,5)$, and explain why the centre of your transformation is the origin.

   [6 marks]

   Total for question 4: 12 marks

End of questions