Henry draws ΔFGH. Then, he translates that triangle to create ΔF'G'H'. The distance from F to F' is 4 centimeters. What is the length of GG'?
A.2 cm
B.3 cm
C.4 cm
D. 6 cm**
I think it's D
all points are moved exactly the same distance. So, not D.
To find the length of GG', we can use the properties of translation.
When a figure is translated, every point on the figure moves the same distance and in the same direction. In this case, the distance from F to F' is given as 4 centimeters.
Since ΔFGH translated to ΔF'G'H', F moves to F' and G moves to G'. Therefore, GG' is the same length as FF', which is 4 centimeters.
Therefore, the length of GG' is 4 centimeters.
So, the correct answer is D. 6 cm is not the correct length.
To find the length of GG', we need to understand the concept of translation and how it affects the positions of the points in a triangle.
Translation is a transformation that moves each point of a shape the same distance and in the same direction. In this case, Henry has translated the triangle ΔFGH to create ΔF'G'H', and the distance from F to F' is given to be 4 centimeters.
Since a translation preserves the length and shape of a triangle, we can conclude that the distance between two corresponding points of the original triangle and its translated image is the same.
Therefore, the distance from G to G' is also 4 centimeters.
So, the length of GG' is 4 centimeters.
The correct answer is option D) 6 cm.