Grade 11 Maths · Functions · Reflect, translate or rotate a point

Transformation of Points Grade 11

Find where a point lands after a reflection, translation or rotation (for example reflecting (2; 5) in the x-axis gives (2; -5)).

questions use it, all grades · 24 past paper, 67 practice: 91 questions use it, all grades · 24 past paper, 67 practice
videos: 4 videos

Learn it: reflect, translate or rotate a point

Pick one and watch it, then try the questions below. Videos load only when you tap play.

Introduction to TRANSFORMATION in Mathematics - Grade 8SHFT - Your Learning

Reflection Across the X and Y Axismrmaisonet

Translating Shapes On The coordinate Plane - Transformationsmrmaisonet

Transformations - Rotate 90 Degrees Around The Originmrmaisonet

Now try it on a real exam question

No sign-up. Takes 3 minutes.

Question 4.5 · May/June 2025 · Paper 2 · National (DBE) · 3 marks

In the diagram, M is the centre of the circle having equation

(x - 3)^{2} + y^{2} = 25

E (- 1; 3)

and T are points on the circle.

EC is a tangent to the circle at E and cuts the x-axis at D.

E D = \frac{15}{4}

units. MT is produced to meet the tangent at

C (- 7; p)

4.5 Calculate the coordinates of S if SEMC is a parallelogram and

x_{S} < 0

.(3)

Work it out on paper first. Then mark yourself with the official memo, one tick at a time.

More past paper questions: reflect, translate or rotate a point

Work each one out first, then open the memo and check every tick.

3. Question 4.1 · November 2024 · Paper 2 · National (DBE) · 2 marks
In the diagram, M $(1; 3)$ is the centre of the circle. The circle cuts the $x$ -axis at N. ST is a tangent to the circle at P $(3; 9)$ . R $(d; 1)$ , with $d > 0$ , and L lie on the circle. O and V are the $x$ -intercepts of PL and RL respectively. $Diagram for this question$
4.1 Write down the coordinates of L.(2)
Show the memo (2 ticks)Memo
1. ✓
  x = −1 $x = - 1$
  1 mark · Reflect, translate or rotate a point
2. ✓
  y = −3 $y = - 3$
  L $(- 1; - 3)$
  1 mark · Reflect, translate or rotate a point
4. Question 5.4 · May/June 2022 · Paper 1 · National (DBE) · 2 marks
Consider: $g (x) = \frac{a}{x + p} + q$

The following information of $g$ is given:
• Domain: $x \in R; x \neq = - 2$
• $x$ -intercept at $K (1; 0)$
• $y$ -intercept at $N (0; - \frac{1}{2})$
5.4 Write down the coordinates of $K^{'}$ , the image of K reflected over $h$ .(2)
Show the memo (2 ticks)Memo
1. ✓
  $x$ -value $K^{'} (- 3; ...)$
  1 mark · Reflect, translate or rotate a point
2. ✓
  $y$ -value $K^{'} (- 3; 4)$
  1 mark · Reflect, translate or rotate a point
5. Question 3.4.1 · May/June 2022 · Paper 2 · National (DBE) · 2 marks
In the diagram, $A (5; 3)$ , $B (0; \frac{1}{2})$ , C and $E (6; - 4)$ are the vertices of a trapezium having $B A ∥ CE$ . D is the $y$ -intercept of CE and $C D = D E$ . $Diagram for this question$
3.4 If point K is the reflection of E in the $y$ -axis:
3.4.1 Write down the coordinates of K(2)
Show the memo (2 ticks)Memo
1. ✓
  x-coordinate of K $x_{K} = - 6$
  1 mark · Reflect, translate or rotate a point
2. ✓
  y-coordinate of K $y_{K} = - 4$
  $K (- 6; - 4)$
  1 mark · Reflect, translate or rotate a point
6. Question 4.6 · May/June 2025 · Paper 1 · National (DBE) · 2 marks
The graph of $f (x) = \frac{4}{x - 3} + 4$ is drawn below. M is the point where the asymptotes of $f$ intersect. C and D are the x- and y-intercepts respectively of $f$ . A is the point on $f$ that is closest to M.
4.6 A single transformation is applied to $f$ to obtain a new graph defined as $h (x) = \frac{- 4}{x + 3} + 4$ . $A^{'}$ is the image of A under this transformation. Calculate the length of $A A^{'}$ .(2)
Show the memo (2 ticks)Memo
1. ✓
  Determine the coordinates of A' $h (x) = \frac{- 4}{x + 3} + 4 = \frac{4}{- x - 3} + 4 = f (- x)$
  This is a reflection across the y-axis.
  $A (5; 6) \to A^{'} (- 5; 6)$
  1 mark · Reflect, translate or rotate a point
2. ✓
  Calculate distance AA'Both points have the same y-coordinate ( $y = 6$ ).
  Distance $= x_{A} - x_{A^{'}} = 5 - (- 5) = 10$
  1 mark · Find a horizontal or vertical length

Free on Android

Know exactly which skill is costing you marks.

Mark past papers tick by tick in the NavyBlue app. It remembers every mark you lose, shows you the skills to fix first, and picks your next questions.

The NavyBlue app showing a learner's weak skills