# Show Hat A(1,2), B(4,3),C(6,6) and D(3,5) Are the Vertices of a Parallelogram. Show that Abcd is Not Rectangle. - Mathematics

Show hat A(1,2), B(4,3),C(6,6) and D(3,5) are the vertices of a parallelogram. Show that ABCD is not rectangle.

#### Solution

The given vertices are  A(1,2), B(4,3),C(6,6) and D(3,5) .

AB = sqrt((1-4)^2+(2-3)^2) = sqrt((-3)^2 +(-1)^2)

= sqrt(9+1) = sqrt(10)

BC = sqrt((4-6)^2 +(3-6)^2) = sqrt((-2)^2 +(-3)^2)

= sqrt(4+9) = sqrt(13)

CD = sqrt((6-3) ^2 +(6-5)^2) = sqrt((3)^2 +(1)^2)

= sqrt(9+1) = sqrt(10)

AD = sqrt((1-3)^2 +(2-5)^2 ) = sqrt((-2)^2 +(-3)^2)

= sqrt(4+9) = sqrt(13)

∵ AB =  CD = sqrt(10) " units and"  BC= AD = sqrt(13)   units

Therefore, ABCD is a parallelogram

AC = sqrt((1-6)^2 +(2-6)^2 )= sqrt((-5)^2 +(-4)^2)

= sqrt(25+16) = sqrt(41)

BD = sqrt((4-3)^2 +(3-5)^2 ) = sqrt((1)^2 +(-2)^2)

= sqrt(1+4) = sqrt(5)

Thus, the diagonal AC and BD are not equal and hence ABCD is not a rectangle

Concept: Coordinate Geometry
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#### APPEARS IN

RS Aggarwal Secondary School Class 10 Maths
Chapter 16 Coordinate Geomentry
Q 31