Question

Figure ABCD is a rectangle whose diagonals intersect at the origin. If point b has the coordinates (a,b), What is the length of diagonal AC?

(Attached Picture)

Answer 1

B

Using pythagoras theorem

`a^(2) + {b}^(2) = {c}^(2)`

`2 {a}^(2) + 2 {b}^(2) = 2 {c}^(2)`
Therefore to find AC (which is 2c)

`2c = \sqrt{2( {a}^(2) + {b}^(2) )}`
Hence it's B.