Question

Triangle DEF has coordinates D(1, 1), E(1, 5), and F(5, 1). Triangle D′E′F′ is the image of ΔDEF by a dilation with center (0, 0) and a scale factor of 7. What is D′F′ ?

Answer 1

To find the image of a point after dilation, you can use the formula:

\[ D'F' = k \cdot DF \]

where \( k \) is the scale factor.

Let's calculate \( DF \), the distance between points D and F:

\[ DF = \sqrt{(x_F - x_D)^2 + (y_F - y_D)^2} \]

\[ DF = \sqrt{(5 - 1)^2 + (1 - 1)^2} = \sqrt{4^2} = 4 \]

Now, use the dilation formula:

\[ D'F' = 7 \cdot DF = 7 \cdot 4 = 28 \]

So, \( D'F' = 28 \).