A translation of 3 units down and 2 units left will shift all the vertices of the polygon downward by 3 units and to the left by 2 units.
- Angle: The angles of the polygon will remain unchanged. Translation does not affect the angles of a shape, so the measures of the angles in the pre-image will be the same as the measures of the corresponding angles in the image.
- Side Lengths: The side lengths of the polygon will remain unchanged. Translation does not affect the lengths of the sides, so the lengths of the sides in the pre-image will be the same as the lengths of the corresponding sides in the image. The distance between any two points on a side of the polygon will be the same before and after the translation.
- Congruency: The pre-image and the image will be congruent. A translation is a rigid transformation that preserves both the angles and the lengths of the sides, so the polygon and its image will be congruent.
In summary, the translation will simply move the entire polygon downward by 3 units and to the left by 2 units, while keeping the angles and side lengths unchanged, resulting in a congruent polygon.
A polygon is shown on the graph:
A polygon is shown on the coordinate plane. Vertices are located at 3 comma 5, 1 comma 3, 1 comma 1, 2 comma 0, 4 comma 0, 5 comma 1, and 5 comma 3.
What effect will a translation 3 units down and 2 units left have on the polygon? Be sure to address how it could impact the angles, side lengths, and congruency between the original pre-image and the image. (5 points)
3 answers
A polygon is shown on the graph:
A polygon is shown on a coordinate plane. The vertices are A at negative 6 comma 5, B at negative 6 comma 2, C at negative 2 comma 2, and D at negative 2 comma 6.
If the polygon is translated 4 units down and 5 units right, what will the coordinates of the new image be? Use prime notation in expressing the new coordinates. (5 points)
A polygon is shown on a coordinate plane. The vertices are A at negative 6 comma 5, B at negative 6 comma 2, C at negative 2 comma 2, and D at negative 2 comma 6.
If the polygon is translated 4 units down and 5 units right, what will the coordinates of the new image be? Use prime notation in expressing the new coordinates. (5 points)
To determine the coordinates of the new image after translating the polygon 4 units down and 5 units right, we need to add 5 to each x-coordinate and subtract 4 from each y-coordinate of the original vertices:
Original vertices:
A: (-6, 5)
B: (-6, 2)
C: (-2, 2)
D: (-2, 6)
New vertices after translation:
A': (-6 + 5, 5 - 4) = (-1, 1)
B': (-6 + 5, 2 - 4) = (-1, -2)
C': (-2 + 5, 2 - 4) = (3, -2)
D': (-2 + 5, 6 - 4) = (3, 2)
The coordinates of the new image are:
A': (-1, 1)
B': (-1, -2)
C': (3, -2)
D': (3, 2)
Therefore, the new image after the translation will have the vertices A' at (-1, 1), B' at (-1, -2), C' at (3, -2), and D' at (3, 2).
Original vertices:
A: (-6, 5)
B: (-6, 2)
C: (-2, 2)
D: (-2, 6)
New vertices after translation:
A': (-6 + 5, 5 - 4) = (-1, 1)
B': (-6 + 5, 2 - 4) = (-1, -2)
C': (-2 + 5, 2 - 4) = (3, -2)
D': (-2 + 5, 6 - 4) = (3, 2)
The coordinates of the new image are:
A': (-1, 1)
B': (-1, -2)
C': (3, -2)
D': (3, 2)
Therefore, the new image after the translation will have the vertices A' at (-1, 1), B' at (-1, -2), C' at (3, -2), and D' at (3, 2).
1 answer