2.3: Coordinate geometry with position vectors

0606/22/M/J/17 — Question 8 · 10 marks

Solutions to this question by accurate drawing will not be accepted.

The points

A

and

B

are

(-8, 8)

and

(4, 0)

respectively.

(i)

Find the equation of the line

AB

[2]

(ii)

Calculate the length of

AB

[2]

(iii)

The point

C

(0, 7)

and

D

is the mid-point of

AB

Show that angle

ADC

is a right angle.

[3]

(iv)

The point

E

is such that

\overrightarrow{AE} = \begin{pmatrix} 4 \\ -7 \end{pmatrix}

Write down the position vector of the point

E

[1]

(v)

Show that

ACBE

is a parallelogram.

[2]