CAIE IGCSE Mathematics Extended 3 Coordinat…metry

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: 6]

(a)

A is the point (1,5) and B is the point (3,9). M is the midpoint of AB.

[ 6 ]

(i)

Find the coordinates of M.

[ 2 ]

(ii)

Find the equation of the line that is perpendicular to AB and passes through M. Give your answer in the form y=m x+c.

[ 4 ]

$y=-\frac{1}{2}x+8$
oe

Correct equivalent in different form scores 3.
M1 for gradient of $AB=\frac{9-5}{3-1}$ , $\frac{4}{2}$ , or 2
M1dep for gradient $p=-\frac{1}{\text{their grad of }AB}$
M1dep for substitution of their midpoint into $y=(\text{their }p)x+c$ oe, where their $p\ne0$

[Maximum number: 3]

Figure for 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: 7]

Figure for 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.

[ 2 ]

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

[ 3 ]

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

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

[Maximum number: 7]

16 A is the point (7,2) and B is the point (-5,8).

(a)

Calculate the length of AB.

[ 3 ]

13.4 or 13.41 to 13.42

M2 for $\sqrt{(-5-7)^2+(8-2)^2}$ oe.
M1 for $(-5-7)^2+(8-2)^2$ oe.

(b)

Find the equation of the line that is perpendicular to AB and that passes through the point (-1,3). Give your answer in the form y=m x+c.

[ 4 ]

y=2x+5 final answer

M1 for gradient of $AB=\frac{8-2}{-5-7}$ oe.
M1 for gradient of perpendicular, $p=-\frac{1}{\text{their gradient}}$ oe.
M1 dep for substituting (-1,3) into $y=\text{their }px+c$ , where their $p\ne0$ .

All question bank results loaded

CAIE IGCSE Mathematics Extended 3 Coordinate Geometry Topic Practice

Covered syllabus points

Question 1

Question (a)

Question (i)

Question (ii)

Question 2

Question 3

Question (a)

Question (b)

Question (c)

Question 4

Question (a)

Question (b)