Question

in the diagram, the right triangles have horizontal and vertical legs, and the hypotenuses lie on the same line. what is the value of ( \frac{gh}{ec} )?

Explanation:

Step1: Find the length of \( GH \)

From the graph, \( G(-2,-3) \) and \( H(-3,-4) \). Using the distance formula for vertical segments (since \( GH \) is vertical), \( GH=\vert - 3-(-4)\vert = 1\) unit.

Step2: Find the length of \( BC \)

From the graph, \( B(6,3) \) and \( C(6,9) \). Using the distance formula for vertical segments (since \( BC \) is vertical), \( BC=\vert9 - 3\vert=6\) units.

Step3: Calculate the ratio \( \frac{GH}{BC} \)

Substitute the values of \( GH = 1 \) and \( BC = 6 \) into the ratio formula. \( \frac{GH}{BC}=\frac{1}{6} \)

Answer:

\(\frac{1}{6}\)