# Show that the Following Points Are the Vertices of a Square: (I) a (3,2), B(0,5), C(-3,2) and D(0,-1) - Mathematics

Show that the following points are the vertices of a square:

(i) A (3,2), B(0,5), C(-3,2) and D(0,-1)

#### Solution

The given points are A (3,2), B(0,5), C(-3,2) and D(0,-1).

AB = sqrt((0-3)^2 +(5-2)^2 ) = sqrt((-3)^2 +(3)^2 ) = sqrt(9+9) = sqrt(18) = 3 sqrt(2) units

BC= sqrt((-3-0)^2 + (2-5)^2) = sqrt((-3)^2 +(3)^2) = sqrt(9+9) = sqrt(18) = 3 sqrt(2)  units

CD = sqrt((0+3)^2 + (-1-2)^2) = sqrt((3)^2 +(-3)^2) = sqrt(9+9) = sqrt(18) = 3 sqrt(2)   units

DA = sqrt((0-3)^2 +(-1-2)^2) = sqrt((-3)^2+(-3)^2) = sqrt(9+9) =sqrt(18) = 3sqrt(2)   units

ThereforeAB =BC=CD=DA=3 sqrt(2)     units

Also, AC = sqrt((-3-3)^2 +(2-2)^2) = sqrt((-6)^2 +(0)^2) = sqrt(36) = 6    units

BD = sqrt((0-0)^2 + (-1-5)^2) = sqrt((0)^2 +(-6)^2 )= sqrt(36) = 6     units

Thus, diagonal AC = diagonal BD

Therefore, the given points from a square.

Concept: Coordinate Geometry
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#### APPEARS IN

RS Aggarwal Secondary School Class 10 Maths
Chapter 16 Coordinate Geomentry
Q 26.1