Question

Use the Polygon tool to draw the image of the given quadrilateral under a dilation with a scale factor of 3/4 and center of dilation ​ (0, 0) ​.

If you could tell me the point that the new quad will be at that would be great!

Answer 1

Given : scale factor(k) =
`(3)/(4)`

Labelled the given diagram as A, B , C and D

Also, From the given quadrilateral figure:

The coordinates are;

A=(-8, 4).

B=(-4, -4),

C=(0, -8) and

D=(4, -4)

The rule of dilation with scale factor k and centered at origin is given by;

`(x, y) \rightarrow (kx, ky)`

or

`(x, y) \rightarrow ((3)/(4)x, (3)/(4)y)`

Then, the coordinates of the dilated given figures are;

`A(-8, 4) \rightarrow ((3)/(4)(-8), (3)/(4)(4)) = A'(-6, 3)`

`B(-4, -4) \rightarrow ((3)/(4)(-4), (3)/(4)(-4)) = B'(-3, -3)`

`C(0, -8) \rightarrow ((3)/(4)(0), (3)/(4)(-8))=C' (0 , -6)`

`D(4, -4) \rightarrow ((3)/(4)(4), (3)/(4)(-4)) = D'(3, -3)`

You can see the graph given below in the attachment