Use mathematical tables to find the reciprocal of 0.0247, hence evaluate [3]3.0250.0247, correct to 2 decimal places.

$$T_x = \frac{nx_1 + mx_2}{m+n} = \frac{1(1) + 2(4)}{2+1} = \frac{1 + 8}{3} = \frac{9}{3} = 3$$ $$T_y = \frac{ny_1 + my_2}{m+n} = \frac{1(-2) + 2(10)}{2+1} = \frac{-2 + 20}{3} = \frac{18}{3} = 6$$

Kuratibu za T ni $\boxed{(3, 6)}$.

Sehemu (b) (i): Tafuta mteremko wa mstari ulio wima kwa PQ

Mteremko wa mstari ulio wima ni hasi ya kinyume cha mteremko wa mstari wa asili.

$$m_{\perp} = -\frac{1}{m_{PQ}} = -\frac{1}{4}$$

Mteremko wa mstari ulio wima kwa PQ ni $\boxed{-\frac{1}{4}}$.

Sehemu (b) (ii): Kuamua mlinganyo wa mstari ulio wima kwa PQ na kupitia T

Tunatumia fomula ya pointi-mteremko: $y - y_1 = m(x - x_1)$.

$$y - 6 = -\frac{1}{4}(x - 3)$$

Panua pande zote mbili kwa 4:

$$4(y - 6) = -(x - 3)$$ $$4y - 24 = -x + 3$$

Panga upya mlinganyo:

$$x + 4y - 24 - 3 = 0$$ $$x + 4y - 27 = 0$$

Mlinganyo wa mstari ni $\boxed{x + 4y - 27 = 0}$.

Sehemu (iii): Kokotoa umbali TR

Kwenye mhimili wa y, $x = 0$. Badilisha $x=0$ kwenye mlinganyo wa mstari $x + 4y - 27 = 0$.

$$0 + 4y - 27 = 0$$ $$4y = 27$$ $$y = \frac{27}{4} = 6.75$$

Kuratibu za R ni $(0, 6.75)$.

$$D = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$ $$D = \sqrt{(0 - 3)^2 + (6.75 - 6)^2}$$ $$D = \sqrt{(-3)^2 + (0.75)^2}$$ $$D = \sqrt{9 + 0.5625}$$ $$D = \sqrt{9.5625}$$ $$D \approx 3.092329$$

Umbali TR, kwa tarakimu tatu muhimu, ni $\boxed{3.09}$.