Q. 29 B

# Prove that the points A (2, 3), B (-2, 2), C (-1, -2), and D (3, -1) are the vertices of a square ABCD.

Answer :

The Vertices of a quadrilateral are A(5,6), B(1,5), C(2,1) and D(6,2).

Using distance formula =

AB = = = units

BC = = = units

CD = = = units

DA = = = units

AB = BC = CD = DA

BD = = = units

AC = = = units

All the four sides of the quadrilateral are equal and diagonals are of equal length. Therefore, the given vertices form a square.

Rate this question :

Using distance formula, examine whether the following sets of points are collinear?

(- 1, 2), (5, 0), (2, 1)

KC Sinha - MathematicsUsing distance formula, examine whether the following sets of points are collinear?

(0, 0), (9, 6), (3, 2)

KC Sinha - MathematicsProve that the distance between the points (a + rcosθ, b + rsinθ) and (a, b) is independent of θ.

KC Sinha - MathematicsUsing distance formula, examine whether the following sets of points are collinear?

(5, 1), (1, - 1), (11, 4)

KC Sinha - MathematicsIf the distances of P(x, y) from points A(3, 6) and B(- 3, 4) are equal, prove that 3x + y = 5

KC Sinha - Mathematics