Question

Each side of a square is of length $4$units . The centre of the square is at $(3,7)$ and one of its diagonals is parallel to $y=x$. Then co-ordinates of its vertices are

• A. $(1,5),(1,9),(8,9),(5,5)$
• B. $(2,5),(2,7),(4,7),(4,4)$
• C. $(2,5),(2,6),(3,5),(3,6)$
• D. $(5,2),(6,2),(5,3),(6,3)$

Answer 1

The correct option is A $(1,5),(1,9),(8,9),(5,5)$

R.E.F image

Let ABCD in square

AB=CD=DA=BC=?

P=(3,7)

draw PM$\perp AB$

M is mid point of AB

So, AM=MB=PM=?

diagonal is parallel to y = x, its sides

are parallel a to coordinate axis

$\therefore$ M = (3, 5)

$\Rightarrow$ A= (3 - 2, 5) = (1, 5)

B = (3 + 2 + 5) = (5, 5)

C = (3 + 5, 7 + 2) = (8, 9)

D = (3 - 2, 7 + 2) = (1, 9)