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
Hector drew ΔNOP with the coordinates (4, 2), (5, 3), and (6,2). Then, he drew an image of this triangle with coordinates (−4,2), (−5,3), and (-6,2). What is the line of reflection for this image?
A.the y-axis
B.the line y = 1
C.the x-axis
D.the line x = 1
B is the right answer
To find the length of GG', we need to understand the concept of translation in geometry. In a translation, every point of the object is moved the same distance and in the same direction. In this case, the distance from F to F' is given as 4 centimeters.
Since the translation is in a straight line, we can understand that both F and F' are on a line parallel to GG'. Therefore, GG' is also 4 centimeters. So, the answer is C. 4 cm.
Now let's move on to the second question.
To find the line of reflection for the image of the triangle with coordinates (-4,2), (-5,3), and (-6,2), we need to understand the concept of reflection.
In reflection, points are mirrored across a line called the line of reflection. The line of reflection acts as a mirror, and on one side of the line, the image is a reflection of the original.
By comparing the original triangle coordinates (4,2), (5,3), and (6,2) with the image coordinates (-4,2), (-5,3), and (-6,2), we can observe that the x-coordinates of the image are negated while the y-coordinates remain the same.
This indicates that the line of reflection is a vertical line passing through the y-axis, which is represented as the equation x = 0. Therefore, the correct answer is A. the y-axis.
To find the length of GG', we need to understand the properties of a translation. When a figure is translated, every point in the figure moves the same distance and in the same direction as every other point.
In this case, since the triangle is translated, we know that GG' is parallel and congruent to FF'. The distance between F and F' is given as 4 centimeters. Therefore, the length of GG' is also 4 centimeters.
So, the correct answer is option C) 4 cm.
For the second question, to determine the line of reflection for the triangle image, we need to identify the transformation that was applied to the original triangle.
The given triangle NOP has the coordinates (4, 2), (5, 3), and (6,2). The image of this triangle has coordinates (-4, 2), (-5, 3), and (-6,2).
To find the line of reflection, we need to observe how the x-coordinates change while the y-coordinates remain the same. In this case, the x-coordinates of the image are the negative values of the x-coordinates of the original triangle.
Since the x-coordinate changes its sign, we can conclude that the line of reflection is the y-axis.
Therefore, the correct answer is option A) the y-axis.