(i)

Refer to graph.

(ii)

$\left(\begin{array}{c}\mathrm{x}\\ \mathrm{y}\end{array}\right)$ + $\left(\begin{array}{c}\mathrm{a}\\ \mathrm{b}\end{array}\right)$ → $\left(\begin{array}{c}\mathrm{x\; +\; a}\\ \mathrm{y\; +\; b}\end{array}\right)$

$\left(\begin{array}{c}2\\ 4\end{array}\right)$ + $\left(\begin{array}{c}-5\\ -2\end{array}\right)$ → $\left(\begin{array}{c}\mathrm{2\; +\; -5}\\ \mathrm{4\; +\; -2}\end{array}\right)$

$\left(\begin{array}{c}2\\ 4\end{array}\right)$ + $\left(\begin{array}{c}-5\\ -2\end{array}\right)$ → $\left(\begin{array}{c}\mathrm{2\; -\; 5}\\ \mathrm{4\; -\; 2}\end{array}\right)$

$\left(\begin{array}{c}2\\ 4\end{array}\right)$ + $\left(\begin{array}{c}-5\\ -2\end{array}\right)$ → $\left(\begin{array}{c}-3\\ 2\end{array}\right)$

A(2,4) → A₁(-3,2)

$\left(\begin{array}{c}2\\ 8\end{array}\right)$ + $\left(\begin{array}{c}-5\\ -2\end{array}\right)$ → $\left(\begin{array}{c}\mathrm{2\; +\; -5}\\ \mathrm{8\; +\; -2}\end{array}\right)$

$\left(\begin{array}{c}2\\ 8\end{array}\right)$ + $\left(\begin{array}{c}-5\\ -2\end{array}\right)$ → $\left(\begin{array}{c}\mathrm{2\; -\; 5}\\ \mathrm{8\; -\; 2}\end{array}\right)$

$\left(\begin{array}{c}2\\ 8\end{array}\right)$ + $\left(\begin{array}{c}-5\\ -2\end{array}\right)$ → $\left(\begin{array}{c}-3\\ 6\end{array}\right)$

B(2,8) → B₁(-3,6)

$\left(\begin{array}{c}8\\ 8\end{array}\right)$ + $\left(\begin{array}{c}-5\\ -2\end{array}\right)$ → $\left(\begin{array}{c}\mathrm{8\; +\; -5}\\ \mathrm{8\; +\; -2}\end{array}\right)$

$\left(\begin{array}{c}8\\ 8\end{array}\right)$ + $\left(\begin{array}{c}-5\\ -2\end{array}\right)$ → $\left(\begin{array}{c}\mathrm{8\; -\; 5}\\ \mathrm{8\; -\; 2}\end{array}\right)$

$\left(\begin{array}{c}8\\ 8\end{array}\right)$ + $\left(\begin{array}{c}-5\\ -2\end{array}\right)$ → $\left(\begin{array}{c}3\\ 6\end{array}\right)$

C(8,8) → C₁(3,6)

$\left(\begin{array}{c}8\\ 4\end{array}\right)$ + $\left(\begin{array}{c}-5\\ -2\end{array}\right)$ → $\left(\begin{array}{c}\mathrm{2\; +\; -5}\\ \mathrm{4\; +\; -2}\end{array}\right)$

$\left(\begin{array}{c}8\\ 4\end{array}\right)$ + $\left(\begin{array}{c}-5\\ -2\end{array}\right)$ → $\left(\begin{array}{c}\mathrm{8\; -\; 5}\\ \mathrm{4\; -\; 2}\end{array}\right)$

$\left(\begin{array}{c}8\\ 4\end{array}\right)$ + $\left(\begin{array}{c}-5\\ -2\end{array}\right)$ → $\left(\begin{array}{c}3\\ 2\end{array}\right)$

D(8,4) → D₁(3,2)

(iii)

y-axis as mirror/reflection in y-asis

$\left(\begin{array}{c}\mathrm{x}\\ \mathrm{y}\end{array}\right)$ → $\left(\begin{array}{c}\mathrm{-x}\\ \mathrm{y}\end{array}\right)$

Thus the x is negated.

$\left(\begin{array}{c}2\\ 4\end{array}\right)$ → $\left(\begin{array}{c}-2\\ 4\end{array}\right)$

A(2,4) → A₂(-2,4)

$\left(\begin{array}{c}2\\ 8\end{array}\right)$ → $\left(\begin{array}{c}-2\\ 8\end{array}\right)$

B(2,8) → B₂(-2,8)

$\left(\begin{array}{c}8\\ 8\end{array}\right)$ → $\left(\begin{array}{c}-8\\ 8\end{array}\right)$

C(8,8) → C₂(-8,8)

$\left(\begin{array}{c}8\\ 4\end{array}\right)$ → $\left(\begin{array}{c}-8\\ 4\end{array}\right)$

D(8,4) → D₂(-8,4)

(i)

Rectangle

(ii)

A₂ = (-2,4)
B₁ = (-3,6)

Gradient = $\frac{\mathrm{Change\; in\; Y}}{\mathrm{Change\; in\; X}}$ = $\frac{{\mathrm{Y}}_2-{\mathrm{Y}}_1}{{\mathrm{X}}_2-{\mathrm{X}}_1}$

Y₂ = 6
Y₁ = 4
X₂ = -3
X₁ = -2

Gradient = $\frac{\mathrm{6-4}}{\mathrm{-3-(-2)}}$ = $\frac{2}{\mathrm{-3+2}}$ = $\frac{2}{-1}$ = -2

(i)

Refer to graph

(ii)

Refer to graph

(i)

y = 10.2 ± 0.2

(ii)

x = 3.9 ± 0.1

(iii)

Use any point on the straight line to calculate for the gradient

Using the points (-1,7) and (1,3)

Gradient = (7-3)/(-1-1)

Gradient = 4/-2 = -2