Question

Draw a quadrilateral of any measurements. Construct a dilation of scale factor 3. Measure their corresponding sides and verify whether they are similar

Answer 1

R.E.F image

Draw a quadrilateral of any

measurement Construct a dilation

Scala factor 3. Measure their

corresponding sides and verily

whether they are similar.

$\to$ Let us consider a quadrilateral (ABCD)

$AB=3cm$ $CD=6cm$

$BC=5cm$ $DA=8cm$

Also in order to find

the length for new quadrilateral

we will use the formula

Now length $=\lambda$ original length

$\lambda$ is dilation factor

and form question $(\lambda =3)$

So for new quadrilateral $\left(A^{\prime }{B}^{\prime }{C}^{\prime }{D}^{\prime }\right)$

$A^1{B}^1=3\times 3=9cm$ $C^1{D}^1=6\times 3=18cm$

$B^1{C}^1=5\times 3=15cm$ $D^1{A}^1=8\times 3=24cm$

For similarity

$AB/A^1{B}^1=CB/C^1{B}^1=CD/C^1{D}^1=AD/A^1{D}^1$

$3/9=5/15=6/18=8/24=1/3$

So both the quadrilateral;

are similar.