Question

Find the centre and length of the diagonal of the square formed by the lines $y=3,x=6,y=7andx=10$

• A. (5, 8) and 4√2
• B. (8, 5) and 4√2
• C. (5, 8) and 2√2
• D. (8, 5) and 2√2
• E. (5, 8) and 4

Answer 1

The correct option is B

(8, 5) and 4√2

Let the centre of the square ABCD be O.
We want to find the coordinates of O and the length of the diagonal (AC or BD).
We can see that the two dotted lines which are parallel to the sides passes through the centre of the circle.

Those lines are marked as x = h and y = k
x = h is the line which is parallel to x = 6 and x = 10 and is equidistant from both.
$\Rightarrow h=\frac{6+10}{2}=8$

$\Rightarrow x=8$ is one of the dotted lines similarly the other line is

$y=\frac{3+7}{2}=5$

$\Rightarrow x=8$ and $y=5$ are the lines passing through O.