Question

triangle abc is congruent to triangle fde, and both triangles have the same orientation, as shown. what is the slope of \\( \overline { d f } \\), which is also the slope of \\( \overline { a c } \\)?

Explanation:

Step1: Find the coordinates of points \(A\) and \(C\)

From the graph, \(A=(1,1)\) and \(C=(3,5)\)

Step2: Use the slope formula \(m = \frac{y_2 - y_1}{x_2 - x_1}\)

Substitute \(x_1 = 1,y_1 = 1,x_2 = 3,y_2 = 5\) into the formula:
\(m=\frac{5 - 1}{3 - 1}\)

Step3: Simplify the expression

\(m=\frac{4}{2}=2\)

Answer:

\(2\)