Answer:
Part a) The length of each of the sides after the dilation is
![A'B'=30\ units](https://img.qammunity.org/2020/formulas/mathematics/middle-school/2yheu07uoytl11zhtceo254gvo2i4by2u6.png)
![B'C'=25\ units](https://img.qammunity.org/2020/formulas/mathematics/middle-school/qoiuqv2v5nsi8sy5tkdqgwlqdmapkntnjv.png)
![A'C'=35\ units](https://img.qammunity.org/2020/formulas/mathematics/middle-school/mnn5c8lpq1b4uvaxeybhjtt8jmmmqjfc5l.png)
Part b) The graph in the attached figure
Explanation:
Part a) What is the length of each of the sides after the dilation?
In this problem we have that the scale factor is 2.5
The scale factor is greater than 1
so
The dilation is an enlargement
To find the length of each of the sides after the dilation, multiply the original length by the scale factor
so
![A'B'=AB*2.5=12*2.5=30\ units](https://img.qammunity.org/2020/formulas/mathematics/middle-school/rp9qzwgke8fx4gnsemcljhruzqctupm8cp.png)
![B'C'=BC*2.5=10*2.5=25\ units](https://img.qammunity.org/2020/formulas/mathematics/middle-school/uhb1m8nencd3dq5i5y2a28l6b34lghc2ts.png)
![A'C'=AC*2.5=14*2.5=35\ units](https://img.qammunity.org/2020/formulas/mathematics/middle-school/3f81b8ev1qhsfae555miie8t9umy9k69y8.png)
Part b) Draw the new image and label it
using a graphing tool
see the attached figure