3.8: Square with diagonal AC and column vectors

0606/22/M/J/21 — Question 6 · 8 marks

The points

A(5, -4)

and

C(11, 6)

are such that

AC

is the diagonal of a square

ABCD

(a)

Find the length of the line

AC

[2]

(b)(i)

The coordinates of the centre

E

of the square are

(8, y)

. Find the value of

y

[1]

(b)(ii)

Find the equation of the diagonal

BD

[3]

(b)(iii)

Given that the

x

-coordinate of

B

is less than that of

D

, write

\overrightarrow{EB}

and

\overrightarrow{ED}

as column vectors.

[2]