Mathematics

Mathematics

Problem

Let

A(0,0)

,

B(6,0)

and

C(4,8)

be the vertices of a triangle. A point

P

inside the triangle is defined by the relation

\overrightarrow{AP}=\dfrac{2}{3}\,\overrightarrow{AB}+\dfrac{1}{3}\,\overrightarrow{AC}

. a. (i) Determine the coordinates of

P

. b. (ii) Find the area of

\triangle ABP

. c. (iii) Hence obtain the ratio

\displaystyle \dfrac{\text{area}(\triangle ABC)}{\text{area}(\triangle ABP)}

.

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