Grade 10 Maths · Analytical Geometry

Reflect, translate or rotate a point

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

past paper questions use it: 8 past paper questions use it
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 1.6 · June 2024 · Paper 2 · Provincial · 2 marks
In the diagram below, $A (- 2; 2)$ , $B (- 4; - 6)$ , $C (4; - 2)$ and $E (6; y)$ are the vertices of a quadrilateral with $A E ∣∣ BC$ . $D$ lies on $BC$ such that $A D ⊥ BC$ and $A C$ is drawn. $M (x; 2)$ is a point on line $EC$ .
1.6 $F$ is a point in the 4th quadrant such that $A BFC$ is a parallelogram. Determine the coordinates of $F$ .(2)
Show the memo (2 ticks)Memo
1. ✓
  x-coordinate of FA $(- 2; 2) \to$ B $(- 4; - 6)$ : $x - 2$ , $y - 8$ . Apply to C $(4; - 2)$ : $x = 4 - 2 = 2$
  1 mark · Reflect, translate or rotate a point
2. ✓
  y-coordinate of F $y = - 2 - 8 = - 10$ , so $F (2; - 10)$
  1 mark · Reflect, translate or rotate a point
4. Question 5.1 · September 2024 · Paper 1 · Provincial · 2 marks
5.1 The point $P (2; 3)$ lies in the Cartesian plane. Determine the coordinates of the image of point P if P is rotated about the origin through $9 0^{0}$ in an anti-clockwise direction.(2)
Show the memo (1 tick)Memo
1. ✓
  Coordinate P' $(- 3; 2)$
  2 marks · Reflect, translate or rotate a point
5. Question 1.4 · June 2024 · Paper 2 · Provincial · 2 marks
In the figure below, $A (- 5; 2)$ and $B (4; - 2)$ are points on a line segment AB.
1.4 Point A undergoes a certain transformation to a point $A^{'}$ such that the gradient of the line $A^{'} B$ becomes undefined. Describe the transformation that maps point A to A'.(2)
Show the memo (1 tick)Memo
1. ✓
  Identify transformationHorizontal transformation of 9 units to the right.
  2 marks · Reflect, translate or rotate a point
6. Question 4.1.3 · March 2018 · Provincial · 2 marks
4.1 $A (p; q), B (2; 4), C (3; 0)$ and $D (- 1; - 2)$ are the vertices of parallelogram ABCD. O is the origin and OE is perpendicular to AB.
4.1.3 Calculate the values of p and q.(2)
Show the memo (1 tick)Memo
1. ✓
  Translate pointMove from C(3;0) to D(-1;-2): Left 4, Down 2.
  Apply to B(2;4): $p = 2 - 4 = - 2$ and $q = 4 - 2 = 2$
  OR use midpoint formula.
  2 marks · Reflect, translate or rotate a point

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