Question

RectangleABCD has vertices A(1, 1) , B(1, 7) , C(3, 7) , and D(3, 1) . A dilation with a scale factor of 0.4 and centered at the origin is applied to the rectangle.

Which vertex in the dilated image has coordinates of (0.4, 2.8) ?

A′

B′

C′

D′

Answer 1

Answer: The correct option is (2) B'.

Step-by-step explanation: Given that the co-ordinates of the vertices rectangle ABCD are A(1, 1) , B(1, 7) , C(3, 7) , and D(3, 1). A dilation with a scale factor of 0.4 and centered at the origin is applied to the rectangle ABCD.

We are to select the correct vertex of the dilated image that has co-ordinates of (0.4, 2.8).

Let, A'B'C'D' be the dilated image of the rectangle after applying a scale factor of 0.4.

We know,

After dilation, each co-ordinate of every vertex of the original rectangle will be multiplied by the scale factor to give the corresponding co-ordinates of the dilated image.

So, we have

`\textup{Co-ordinates of }A'=0.4* \textup{co-ordinates of A}=0.4*(1,1)=(0.4,0.4),\\\\\textup{Co-ordinates of }B'=0.4* \textup{co-ordinates of B}=0.4*(1,7)=(0.4,2.8),\\\\\textup{Co-ordinates of }C'=0.4* \textup{co-ordinates of C}=0.4*(3,7)=(1.2,2.8),\\\\\textup{Co-ordinates of }D'=0.4* \textup{co-ordinates of D}=0.4*(3,1)=(1.2,0.4).`

So, the co-ordinates of the vertex B' are (0.4, 2.8).

Thus, option (2) is correct.