Grade 10 Maths · Analytical Geometry

Calculate distance between two points

Find the length between two points using the distance formula, for example (1; 2) and (4; 6) are √(3² + 4²) = 5 units apart.

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Analytical Geometry Grade 10: Distance formulaKevinmathscience

Analytical Geometry Grade 10: Distance formula - length of a lineMiss Martins Maths and Science

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How To Find The Distance Between Two PointsThe Organic Chemistry Tutor

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Question 3.2 · May/June 2025 · Paper 2 · National (DBE) · 3 marks

In the diagram below,

Δ SRT

is drawn where R lies on the x-axis and S lies to the left of R. T lies on the y-axis and the coordinates of S are

(m; 1)

.

The equation of RT is

2 x - y + 10 = 0

3.2 Calculate the length of RT. Leave your answer in surd form.(3)

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

More past paper questions: calculate distance between two points

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3. Question 1.1 · June 2024 · Paper 2 · Provincial · 3 marks
In the figure below, $A (- 5; 2)$ and $B (4; - 2)$ are points on a line segment AB.
1.1 Determine the length of AB.(3)
Show the memo (2 ticks)Memo
1. ✓
  Substitute coordinates into distance formula $A B = (x_{A} - x_{B})^{2} + (y_{A} - y_{B})^{2}$
  $A B = (- 5 - 4)^{2} + (2 - (- 2))^{2}$
  2 marks · Calculate distance between two points
2. ✓
  Calculate final length $A B = (- 9)^{2} + (4)^{2}$
  $A B = 81 + 16$
  $A B = 97$
  1 mark · Calculate distance between two points
4. Question 1.1 · June 2024 · Paper 2 · Provincial · 4 marks
$PQRS$ is a quadrilateral with vertices $P (- 5; 0)$ , $Q (0; t)$ , $R (3; - 2)$ and $S (- 2; - 5)$ .
$P$ is on the x-axis and $Q$ is on the y-axis.
1.1 Determine the lengths of $PS$ and $RS$ .(4)
Show the memo (4 ticks)Memo
1. ✓
  Substitution into the distance formula for PS $PS = (- 2 + 5)^{2} + (- 5 - 0)^{2}$
  1 mark · Calculate distance between two points
2. ✓
  Length of PS $PS = 34$
  1 mark · Calculate distance between two points
3. ✓
  Substitution into the distance formula for RS $RS = (3 + 2)^{2} + (- 2 + 5)^{2}$
  1 mark · Calculate distance between two points
4. ✓
  Length of RS $RS = 34$
  1 mark · Calculate distance between two points
5. Question 4.1.1 · 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.
4.1.1 Calculate the length of DC. (leave your answer in surd form)(2)
Show the memo (2 ticks)Memo
1. ✓
  Distance formula $D C = (3 - (- 1))^{2} + (0 - (- 2))^{2}$
  1 mark · Calculate distance between two points
2. ✓
  Calculate $= 4^{2} + 2^{2} = 20$
  1 mark · Calculate distance between two points
6. Question 3.1.1 · March 2016 · Provincial · 4 marks
3.1 In the diagram below, ABCD is a quadrilateral with $A (3; 11)$ , $B (0; 2)$ , $C (3; 1)$ , $D (7; 3)$ .
3.1.1 Calculate the lengths of AB and AD.(4)
Show the memo (4 ticks)Memo
1. ✓
  AB substitution $A B = (3 - 0)^{2} + (11 - 2)^{2} = 9 + 81$
  1 mark · Calculate distance between two points
2. ✓
  AB simplified $A B = 90 = 310$
  1 mark · Calculate distance between two points
3. ✓
  AD substitution $A D = (7 - 3)^{2} + (3 - 11)^{2} = 16 + 64$
  1 mark · Calculate distance between two points
4. ✓
  AD simplified $A D = 80 = 45$
  1 mark · Calculate distance between two points

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