the triangle ( lmn ) is a dilation of the triangle ( lmn ). what is the scale factor of the…

the triangle ( lmn ) is a dilation of the triangle ( lmn ). what is the scale factor of the dilation?\nsimplify your answer and write it as a proper fraction, an improper fraction, or a whole number.

the triangle ( lmn ) is a dilation of the triangle ( lmn ). what is the scale factor of the dilation?\nsimplify your answer and write it as a proper fraction, an improper fraction, or a whole number.

Answer

Explanation:

Step1: Find the length of corresponding sides

Let's consider side (NN'). Point (N=(0,1)) and (N'=(0,4)). The length of (NN' = 4 - 1=3). Point (M=(0,0)) and (M'=(0, - 4)). The length of (MM'=|0-(-4)| = 4) (but we can also use another pair. Let's use (LN) and (L'N'). Coordinates of (L=(-1,1)), (N=(0,1)), so (LN=\sqrt{(0 - (-1))^{2}+(1 - 1)^{2}}=1). Coordinates of (L'=(-4,4)), (N'=(0,4)), so (L'N'=\sqrt{(0-(-4))^{2}+(4 - 4)^{2}}=4).

Step2: Calculate the scale factor

The scale factor (k) of a dilation is given by the ratio of the length of a side of the dilated figure ((L'M'N')) to the length of the corresponding side of the original figure ((LMN)). Using (LN = 1) (original side) and (L'N'=4) (dilated side), the scale factor (k=\frac{L'N'}{LN}) Since (L'N' = 4) and (LN = 1), (k = 4)

Answer:

(4)