the triangle jkl is a dilation of the triangle jkl. what is the scale factor of the dilation? simplify your…
the triangle jkl is a dilation of the triangle jkl. what is the scale factor of the dilation? simplify your answer and write it as a proper fraction, an improper fraction, or a whole number.
Answer
Explanation:
Step1: Identify corresponding side - lengths
Let's consider the vertical distance from (J) to (L) and (J') to (L'). The coordinates of (J=(0, - 2)), (L=(0,2)), so the length of (JL) is (|2-(-2)| = 4). The coordinates of (J'=(-5,-10)), (L'=(-5,10)), so the length of (J'L') is (|10 - (-10)|=20).
Step2: Calculate the scale - factor
The scale factor (k) of a dilation is given by the ratio of the length of a side in the dilated figure to the length of the corresponding side in the original figure. So (k=\frac{J'L'}{JL}). Substituting the values we found: (k = \frac{20}{4}=5).
Answer:
5