Question

triangle abc is similar to triangle def. write the equation, in slope - intercept form, of the side of triangle def that is parallel to \\(\overline{bc}\\). you must show all work to receive credit.

Explanation:

Step1: Find the slope of \(\overline{BC}\)

Use the slope formula \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let \(B(-3,4)\) and \(C(0,1)\). Then \(m_{BC}=\frac{1 - 4}{0-(-3)}=\frac{-3}{3}=- 1\).

Step2: Determine the parallel side in \(\triangle DEF\)

Since \(\triangle ABC\sim\triangle DEF\), the side parallel to \(\overline{BC}\) is \(\overline{EF}\).

Step3: Find a point on \(\overline{EF}\)

Let \(E(2,3)\) and \(F(4,1)\). We can also use the slope - intercept form \(y = mx + b\). We know \(m=-1\) (parallel lines have equal slopes). Using the point \(E(2,3)\) and \(y=-x + b\), substitute \(x = 2\) and \(y = 3\) into the equation: \(3=-2 + b\), so \(b = 5\).

Answer:

\(y=-x + 5\)