Question

$\overline{fg}$ is shown on the graph below. $\overline{fg}$ is dilated by a scale factor of 5 centered at the origin to create $\overline{fg}$.

(graph with points f and g on a coordinate plane, f at (-8, 9), g at (-2, 1))

what is the length of $\overline{fg}$?

write your answer as a whole number or as a decimal rounded to the nearest tenth.

units

Explanation:

Step1: Find coordinates of F and G

From the graph, \( F(-8, 9) \), \( G(-2, 1) \).

Step2: Calculate length of FG using distance formula

Distance formula: \( d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \)
Substitute \( x_1=-8, y_1=9, x_2=-2, y_2=1 \):
\( FG = \sqrt{(-2 - (-8))^2 + (1 - 9)^2} = \sqrt{(6)^2 + (-8)^2} = \sqrt{36 + 64} = \sqrt{100} = 10 \)

Step3: Find length of F'G' after dilation

Dilation scale factor \( k = 5 \), so \( F'G' = k \times FG = 5 \times 10 = 50 \)

Answer:

50