Question

A triangle is dilated using a scale factor of $3$. The image is then dilated using a scale factor of $\frac{1}{2}$. What scale factor can you use to dilate the original triangle to obtain the final image? Explain.

Answer 1

Check the scale factor of dilation for original triangle.

As we have given,

First scale factor of triangle, ${\mathrm{S}}_1=3$

Second scale factor of triangle, ${\mathrm{S}}_2=\frac{1}{2}$

As we know that the final scale factor, $\mathrm{S}={\mathrm{S}}_1\times {\mathrm{S}}_2$

So, final scale factor, $\mathrm{S}=3\times \frac{1}{2}=\frac{3}{2}$

Hence, the scale factor of the final image will be the multiplication of the first and second dilation scale factor and the final scale factor will be $\frac{3}{2}$.