Question

The diagram shows two quadrilaterals graphed on a coordinate plane. 4 5 6 7 8 Which transformation on quadrilateral 1 can be used to verify that is similar to quadrilateral

Answer 1

dilation, k=0.5

Step-by-step explanation

Step 1

as we can see, the quadrilaterals have different size. it means we can discard a traslation

Step 2

now, we can see both quadrilateral have similar shape, so we can check for a dilation.

A dilation is a type of transformation that changes the size of the image. The scale factor measures how much larger or smaller the image is

`A(x,y)\rightarrow Dilation\rightarrow A^(\prime)(kx,ky)`

in this case, quadrilateral 1 is bigger than quadrilateral 2, it means it suffered a compresion, so k is smaller than 1

`A(x,y)\rightarrow A^(\prime)(kx,ky)\text{ for k}<1`

we can find k,

let

A=a point of the quadrilateral

`\begin{gathered} A(-6,0)\rightarrow A^(\prime)(-6k,0k)\rightarrow A^(\prime)(-3,0) \\ so \\ -6k=-3 \\ k=(-3)/(-6) \\ k=(1)/(2) \end{gathered}`

I hope this helps you