Respuesta :
Answer:
The parallelogram is translated about 6.33 units far, 2 units left and 4 units downwards
Explanation:
Given:
The coordinates of the vertices of the preimage of the parallelogram are:
(1,5), (3,3), (3,7), and (5,5)
The coordinates of the vertices of the image are:
(-5,3), (-3,1), (-3,5), and (-1,3).
We want to know how far and in what direction the parallelogram was translated.
Looking at the given coordinates, we see that there is an equal distance between a coordinate in the image with the corresponding image.
(1,5) and (-5,3)
(3,3) and (-3,1)
(3,7) and (-3,5)
(5,5) and (-1,3)
all have equal distances between them.
So, knowing the distance of one suffices for all.
The distance between two points is given by the formula:
[tex]D=\sqrt[]{(y_2-y_{1)^2}+(x_2-x_1)^2}[/tex]Using the coordinates (1,5) and (-5,3)
[tex]\begin{gathered} x_1=1 \\ y_1=5 \\ x_2=-5 \\ y_2=3 \end{gathered}[/tex]So
[tex]\begin{gathered} D=\sqrt[]{(3-5)^2+(-5-1)^2} \\ \\ =\sqrt[]{(-2)^2+(-6)^2} \\ \\ =\sqrt[]{4+36} \\ \\ =\sqrt[]{40} \\ \\ =6.33\text{ units} \end{gathered}[/tex]The Direction:
The translation is 2 units left, and 4 units downward
