NCERT Example 2 — Coordinate Geometry

NCERT Example

Example 2

distance formula · square · diagonals

Show that the points A(1, 7), B(4, 2), C(-1, -1) and D(-4, 4) are the vertices of a square.

Board-exam working:

Using the distance formula for each side:

AB=\sqrt{(4-1)^2+(2-7)^2}=\sqrt{9+25}=\sqrt{34}

BC=\sqrt{(-1-4)^2+(-1-2)^2}=\sqrt{25+9}=\sqrt{34}

CD=\sqrt{(-4-(-1))^2+(4-(-1))^2}=\sqrt{9+25}=\sqrt{34}

DA=\sqrt{(1-(-4))^2+(7-4)^2}=\sqrt{25+9}=\sqrt{34}

Now calculate the diagonals:

AC=\sqrt{(-1-1)^2+(-1-7)^2}=\sqrt{4+64}=\sqrt{68}

BD=\sqrt{(-4-4)^2+(4-2)^2}=\sqrt{64+4}=\sqrt{68}

AB=BC=CD=DA

AC=BD

All four sides are equal and both diagonals are equal. Therefore, ABCD is a square.

ABCD is a square.