With reference to the conventional Cartesian $(\mathrm{x}, \mathrm{y})$ coordinate system, the vertices of a triangle have the following coordinates: $\left(\mathrm{x}_{1}, \mathrm{y}_{1}\right)=(1,0) ;\left(\mathrm{x}_{2}, \mathrm{y}_{2}\right)=(2,2) ;$ and $\left(\mathrm{x}_{3}, \mathrm{y}_{3}\right)=(4,3) .$ The area of the triangle is equal to

(A) $\frac{3}{2}$

(B) $\frac{3}{4}$

(C) $\frac{4}{5}$

(D) $\frac{5}{2}$

With reference to the conventional Cartesian $(\mathrm{x}, \mathrm{y})$ coordinate system, the vertices of a triangle have the following coordinates: $\left(\mathrm{x}_{1}, \mathrm{y}_{1}\right)=(1,0) ;\left(\mathrm{x}_{2}, \mathrm{y}_{2}\right)=(2,2) ;$ and $\left(\mathrm{x}_{3}, \mathrm{y}_{3}\right)=(4,3) .$ The area of the triangle is equal to

(A) $\frac{3}{2}$

(B) $\frac{3}{4}$

(C) $\frac{4}{5}$

(D) $\frac{5}{2}$

Match the information given in Group I with those in Group - II.

Group I Group II

P Factor to decrease ultimate strength to 1 Upper bound on ultimate load design strength

Q Factor to increase working load to 2 Lower bound on ultimate load ultimate load for design

R Statical method of ultimate load 3 Material partial safety factor analysis

S Kinematical mechanism method of 4 Load factor ultimate load analysis

(A) $P-1 ; Q-2 ; R-3 ; S-4$

(B) $P-2 ; Q-1 ; R-4 ; S-3$

(C) $\mathrm{P}-3 ; \mathrm{Q}-4 ; \mathrm{R}-2 ; \mathrm{S}-1$

(D) $\mathrm{P}-4 ; \mathrm{Q}-3 ; \mathrm{R}-2 ; \mathrm{S}-1$

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