3.22: Point dividing AC and perpendicular through B

0606/11/O/N/21 — Question 2 · 6 marks

Points

A

and

C

have coordinates

(-4, 6)

and

(2, 18)

respectively. Point

B

lies on

AC

such that

\overrightarrow{AB} = \dfrac{2}{3}\overrightarrow{AC}

(a)

Find the coordinates of

B

[2]

(b)

Find the equation of the line

\ell

which is perpendicular to

AC

and passes through

B

[2]

(c)

Find the area enclosed by the line

\ell

and the coordinate axes.

[2]