CAIE IGCSE Mathematics Extended Coordinate Geometry Question Bank

Practise coordinates, gradients, straight-line equations, parallel and perpendicular lines, midpoints and distances across coordinate geometry.

Covered syllabus points

E3.1 Coordinates E3.2 Drawing linear graphs E3.3 Gradient of linear graphs E3.4 Length and midpoint E3.5 Equations of linear graphs E3.6 Parallel lines E3.7 Perpendicular lines

[Maximum number: 8]

(a)

In the square A B C D, A has coordinates (-2,1) and B has coordinates (1,5). C has coordinates (a, b), where a and b are both positive integers.

Find the coordinates of C and the coordinates of D.
You may use the grid to help you.

Figure for Question (a) — CAIE IGCSE Mathematics Extended

(b)

P has coordinates (-1,3) and Q has coordinates (6,4).

[ 8 ]

(i)

Find the coordinates of the midpoint of PQ.

[ 2 ]

(ii)

Find the length PQ.

[ 3 ]

7.07 or 7.071...
M2 for $(6-(-1))^2+(4-3)^2$ oe, or M1 for 6-(-1) or 4-3 oe

(iii)

Find the equation of the line parallel to PQ that crosses the x-axis at x=2.

[ 3 ]

$y=\frac17x-\frac27$ or 7y=x-2 oe final answer
M1 for gradient = their (iii)
M1dep for substituting (2,0) in a linear equation with their gradient

[Maximum number: 3]

Figure for Question 3. Coordinate geometry question 2 — CAIE IGCSE Mathematics Extended

On the grid, draw the lines y=x and x+y=7.

$\begin{aligned}y&=x\text{ ruled}\\x+y&=7\text{ ruled}\end{aligned}$

B1 for y=x.
B2 for x+y=7, or B1 for a ruled line with gradient -1, or through (0,7) or (7,0), but not x=7 or y=7.

[Maximum number: 2]

Figure for Question 3. Coordinate geometry question 3 — CAIE IGCSE Mathematics Extended

(a)

Find the gradient of line l.

[ 2 ]

$-\frac{3}{4}$ or -0.75

M1 for correct rise over run
or B1 for answer $\frac{3}{4}$ oe

(b)

Find the equation of line l in the form y=m x+c.

$y=-\frac{3}{4}x+2$ oe

FT their (a) x+2 oe
B1 for their (a) x+c or mx+2

(c)

Find the equation of the line that is perpendicular to line l and passes through the point (12,-7). Give your answer in the form y=m x+c.

$y=\frac{4}{3}x-23$ oe

M1 for gradient $\frac{-1}{\text{their (a)}}$
M1 for (12,-7) substituted into y= their mx+c

[Maximum number: 2]

Figure for Question 3. Coordinate geometry question 4 — CAIE IGCSE Mathematics Extended

Write down the equation of your tangent in the form y=m x+c.

$y=(4.4\text{ to }5.6)x-(1.8\text{ to }2.2)$
OR y= their (b)(ii) x+ their y-intercept.
FT for any line but not horizontal or vertical for 2 marks.
B1FT for m= their gradient or for their y-intercept.

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Covered syllabus points

3. Coordinate geometry question 1

Question (a)

Question (b)

Question (i)

Question (ii)

Question (iii)

3. Coordinate geometry question 2

3. Coordinate geometry question 3

Question (a)

Question (b)

Question (c)

3. Coordinate geometry question 4