Question

STATEMENT -1 : Points (1, 7), (4, 2), (-1, -1) and (-4, 4) are the vertices of a square.
STATEMENT - 2 : The distance between $P(x_1,y_1)$ and $Q(x_2,y_2)$ is $\sqrt{(x_2-x_1{)}^2+(y_2-y_1{)}^2}$. So for a square all length of all sides should be same.

• A. Statement - 1 is True, Statement - 2 is True, Statement - 2 is a correct explanation for Statement - 1
• B. Statement - 1 is True, Statement - 2 is True : Statement 2 is NOT a correct explanation for Statement - 1
• C. Statement - 1 is True, Statement - 2 is False
• D. Statement - 1 is False, Statement - 2 is True

Answer 1

Answer: (A)

Statement - 1 is True, Statement - 2 is True, Statement - 2 is a correct explanation for Statement - 1

Let the points $A(1,7),B(4,2),C(-1,-1)$ and $(-4,4)$ are the vertices of a quadrilateral $ABCD$.

So, by distance formula, we have

$AB=\sqrt{(4-1{)}^2+(2-7{)}^2}=6$
$BC=\sqrt{(-1-4{)}^2+(-1-2{)}^2}=6$
$CD=\sqrt{(-4+1{)}^2+(4+1{)}^2}=\sqrt{9+25}=6$
$DA=\sqrt{(-4-1{)}^2+(4-7{)}^2}=\sqrt{25+9}=6$

Thus, all the distances are same, hence given points are the vertices of a square.