Dilate a triangle with vertices (0,0), (0,2) and (2,0) using the scale factor k=3. What is the value of the ratio (new to original) of the perimeters? the areas?The ratio of the perimeters is ___.The ratio of the areas is ___.
Accepted Solution
A:
Answer:Part a) The ratio of the perimeters is [tex]3[/tex]Part b) The ratio of the areas is [tex]9[/tex]Step-by-step explanation:Part A) What is the value of the ratio (new to original) of the perimeters?we know thatIf two figures are similar, then the ratio of its perimeters is equal to the scale factorLetz-----> the scale factorx-----> the perimeter of the new triangley-----> the perimeter of the original triangle[tex]z=\frac{x}{y}[/tex]we have[tex]z=3[/tex]substitute[tex]\frac{x}{y}=3[/tex]Part B) What is the value of the ratio (new to original) of the areas?we know thatIf two figures are similar, then the ratio of its areas is equal to the scale factor squaredLetz-----> the scale factorx-----> the area of the new triangley-----> the area of the original triangle[tex]z^{2}=\frac{x}{y}[/tex]we have[tex]z=3[/tex]substitute[tex]\frac{x}{y}=3^{2}[/tex][tex]\frac{x}{y}=9}[/tex]