Question

If ∆ABC = ∆EDF where the coordinates of A(0,2), B(2,4), and C(2,-1), what is the measure of DF?A-3B-3.1C-5D-5.9Please respond quickly

Answer 1

The triangles ABC and EDF are congruent, meaning they have the same side lengths and angles measures.

The measure of DF, as both triangles are congruent, is equal to the measure of BC.

We can calculate the length of BC using the distance formula:

$\begin{gathered} D=\sqrt[]{(x_c-x_b)^2+(y_c-y_b_{})^2} \\ D=\sqrt[]{(2-2)^2+(-1-4)^2} \\ D=\sqrt[]{0^2+(-5)^2} \\ D=\sqrt[]{(-5)^2} \\ D=|-5| \\ D=5 \end{gathered}$

As BC is congruent with DF and BC=5, the length of DF is 5 units.