Answer:
DF = 3
Step-by-step explanation:
If ABC is equivalent to EDF, then DF is equivalent to BC, which form the following ordered pairs:
D = (0,2)
F = (3,2)
It can be seen that both pairs have the same value of "y" or second value, that is 2.
As a rule, when the points are located on the y-axis (of the ordinates) or on a line parallel to this axis, the distance between the points corresponds to the absolute value of the difference of their ordinates.
So,
DF = D(x) + F(x) = 0 + 3 = 3
If we apply the equation of the distance between two points we get the same result,
![DF=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2} }=\sqrt{(3-0)^{2}+(2-2)^{2} }=\sqrt{(3)^{2}+(0)^{2} }=\sqrt{9+0 }=\sqrt{9}=3](https://tex.z-dn.net/?f=DF%3D%5Csqrt%7B%28x_%7B2%7D-x_%7B1%7D%29%5E%7B2%7D%2B%28y_%7B2%7D-y_%7B1%7D%29%5E%7B2%7D%20%20%20%7D%3D%5Csqrt%7B%283-0%29%5E%7B2%7D%2B%282-2%29%5E%7B2%7D%20%20%20%7D%3D%5Csqrt%7B%283%29%5E%7B2%7D%2B%280%29%5E%7B2%7D%20%20%20%7D%3D%5Csqrt%7B9%2B0%20%20%20%7D%3D%5Csqrt%7B9%7D%3D3)
Hope this helps!