Question

One end of a diagonal of a square is $(2,0)$ and its slope is $1$. If the length of the side of a square is $2$ units, then write all the possible coordinates of the other end.

• A. $(4,2)$
• B. $(0,2)$
• C. $(2,4)$
• D. $(-2,0)$

Answer 1

The correct option is A $(4,2)$

Given

One end of diagonal of square is $(2,0)$ and slope is 1

Let other end of diagonal is $(x,y)$

then $m=1$

$1=\frac{y}{x-2}$

$x-2=y$----(1)

The length of side of square is 2 hence

By pythagoras theoram length of diagonal be $\sqrt{8}$

$\sqrt{(x-2{)}^2+y^2}=\sqrt{8}$

On squaring both sides

$(x-2{)}^2+y^2=8$

from eq (1)

$2y^2=8$

$y^2=4$

$y=\pm 2=2,-2$

$x=4,0$

Possible coordinates are $(4,2)$ and $(0,-2)$