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

Answer:

Given : scale factor(k) = $\frac{3}{4}$

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

$(x, y) \rightarrow (\frac{3}{4}x, \frac{3}{4}y)$

Then, the coordinates of the dilated given figures are;

$A(-8, 4) \rightarrow (\frac{3}{4}(-8), \frac{3}{4}(4)) = A'(-6, 3)$

$B(-4, -4) \rightarrow (\frac{3}{4}(-4), \frac{3}{4}(-4)) = B'(-3, -3)$

$C(0, -8) \rightarrow (\frac{3}{4}(0), \frac{3}{4}(-8))=C' (0 , -6)$

$D(4, -4) \rightarrow (\frac{3}{4}(4), \frac{3}{4}(-4)) = D'(3, -3)$

You can see the graph given below in the attachment