CAIE IGCSE Mathematics Extended 3 Coordinate Geometry Topic Practice

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

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

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

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

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

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

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.

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 $p\ne0$.

$[AB^2=](3-0)^2+(3-2)^2$ oe or better, or $\begin{pmatrix}3\\1\end{pmatrix}$ oe
$[AC^2=](4-0)^2+(0-2)^2$ oe or better
$[BC^2=](4-3)^2+(0-3)^2$ oe or better
Triangle is isosceles [with 10, 10, 20]

$y=-\frac12x+2$ oe
M1 for $\frac{0-2}{4-0}$ oe
M1 for substituting (0,2) or (4,0) into y= their mx+c oe
or B1 for answer y=kx+2

y=2x-3
M1 for $\frac{-1}{\text{their grad }(b)(i)}$
B1 for (2,1)
M1 for substituting their (2,1) into y= their px+d oe

(-2,-7)
B2 for w=-2
or M1 for 4w+1=2w-3 FT their (b)(ii) or for $2=\frac{4w+1-3}{w-3}$