Question

If A(6, 1), B(8, 2), C(9, 4) and D(7, 3) are the vertices of `square`ABCD, show that `square`ABCD is a parallelogram.

Solution:

Slope of line = `("y"_2 - "y"_1)/("x"_2 - "x"_1)`

∴ Slope of line AB = `(2 - 1)/(8 - 6) = square` .......(i)

∴ Slope of line BC = `(4 - 2)/(9 - 8) = square` .....(ii)

∴ Slope of line CD = `(3 - 4)/(7 - 9) = square` .....(iii)

∴ Slope of line DA = `(3 - 1)/(7 - 6) = square` .....(iv)

∴ Slope of line AB = `square` ......[From (i) and (iii)]

∴ line AB || line CD

∴ Slope of line BC = `square` ......[From (ii) and (iv)]

∴ line BC || line DA

Both the pairs of opposite sides of the quadrilateral are parallel.

∴ `square`ABCD is a parallelogram.

Answer 1

Slope of line = `("y"_2 - "y"_1)/("x"_2 - "x"_1)`

∴ Slope of line AB = `(2 - 1)/(8 - 6) = 1/2` .......(i)

∴ Slope of line BC = `(4 - 2)/(9 - 8) = 2` .....(ii)

∴ Slope of line CD = `(3 - 4)/(7 - 9) = 1/2` .....(iii)

∴ Slope of line DA = `(3 - 1)/(7 - 6) = 2` .....(iv)

∴ Slope of line AB = Slope of line CD ......[From (i) and (iii)]

∴ line AB || line CD

∴ Slope of line BC = Slope of line DA ......[From (ii) and (iv)]

∴ line BC || line DA

Both the pairs of opposite sides of the quadrilateral are parallel.

∴ `square`ABCD is a parallelogram.