Question

Graph the image of this figure after a dilation with a scale factor of 12 centered at the point (2, 2) . Use the polygon tool to graph the dilated figure.

Answer 1

Answer:

Labelled the given figure triangle as A, B and C.

In triangle ABC;

The coordinates of ABC are:

A = (0, 4)

B = (-2, 10) and

C = (-6, 8)

To find the image of this figure after a dilation with a scale factor of $\frac{1}{2}$ centered at the point O=(2, 2).

The rule of dilation with scale factor $\frac{1}{2}$ centered at the point (2, 2) is given by;

$(x, y) \rightarrow (\frac{1}{2}(x-2) +2 , \frac{1}{2}(y-2) +2)$

or

$(x, y) \rightarrow (\frac{1}{2}x+1 , \frac{1}{2}y+1)$

The coordinate of the image of the figure after dilation are;

$A(0, 4) \rightarrow A'(\frac{1}{2}(0)+1 , \frac{1}{2}(4)+1)$ = A'(1, 3)

$B(-2, 10) \rightarrow B'(\frac{1}{2}(-2)+1 , \frac{1}{2}(10)+1)$ = B'(0, 6)

$C(-6, 8) \rightarrow C'(\frac{1}{2}(-6)+1 , \frac{1}{2}(8)+1)$ = C'(-2, 5)

You can see the graph as shown below in the attachment: