a dilation centered at the origin is applied to figure a. the result is figure b. what is the scale factor…
a dilation centered at the origin is applied to figure a. the result is figure b. what is the scale factor of the dilation? write your answer as a whole number or a fraction in simplest form.
Answer
Explanation:
Step1: Select corresponding lengths
Choose a side - length in Figure A and its corresponding side - length in Figure B. For example, if we consider the base of the triangles. Let's assume the base of Figure A has a length of 2 units (by counting grid squares), and the base of Figure B has a length of 6 units.
Step2: Calculate scale factor
The scale factor $k$ of a dilation is given by the ratio of the length of a side in the dilated figure (Figure B) to the length of the corresponding side in the original figure (Figure A). So, $k=\frac{\text{length in Figure B}}{\text{length in Figure A}}=\frac{6}{2}$.
Step3: Simplify the ratio
$\frac{6}{2} = 3$.
Answer:
3