Translations - Draw
Draw (-3, 4) and then translate it 4 units to the left. Draw the image and pre-image. Label them as such.
(-7, 4)
Suppose the point (x,y) is translated horizontally c units. How do you know the point is translated left or right?
Negative = left, Positive = right
Draw (-3, 4) and then reflect it across the x-axis. Draw the image and pre-image. Label them as such.
(-3, -4)
Suppose the point (x,y) is translated across an axis. How do you know which axis?
If the x changes, then it's the y-axis. If the y changes, then it's the x-axis.
Point (2, 3) is reflected across the y-axis and translated up 1. Write the coordinate for the image.
(-2, 4)
Draw (-3, 4) and then translate it 4 units up. Draw the image and pre-image. Label them as such.
(-3, 8)
Suppose the point (x,y) is translated vertically d units. How do you know if the point is translated up or down?
Negative = down, Positive = up
Draw (-3, 4) and then reflect it across the y-axis. Draw the image and pre-image. Label them as such.
(3, 4)
Suppose the point (m, n) is reflected across the x-axis. Write the coordinates of the image of the point.
(m, -n)
How can you use translations or reflections to prove congruency?
If all points get translated or reflected the same, then the shapes are congruent.
Stephanie drew a triangle with vertices at (1, 2), (3, 3), and (4, 1). She slides the triangle 2 units down to create an image. What are the vertices of the image?
(1, 0), (3, 1), (4, -1)
Suppose the point (m, n) is translated horizontally c units. Write the coordinates of the image of the point.
(m+c, n)
Stephanie drew a triangle with vertices at (1, 2), (3, 3), and (4, 1). She reflects the triangle across the x-axis to create an image. What are the vertices of the image?
(1, -2), (3, -3), and (4, -1)
Suppose the point (r, s) is reflected across the y-axis. Write the coordinates of the image of the point.
(-r, s)
John draws a square on a coordinate plane. Then, he draws an image of the square 3 units to the right of the original square. What is true about the corresponding sides on the original figure and the image?
a. The corresponding sides intersect at one point.
b. The corresponding sides intersect at an infinite number of points.
c. The corresponding sides are parallel.
C
Blake drew square ABCD. Then, he drew the image of it, square A'B'C'D', 2 centimeters to the right of the original figure. Line segment BC is 3 centimeters. How long is B'C'? How do you know?
3 cm - congruent figures
Suppose the point (r, s) is translated vertically d units. Write the coordinates of the image of the point.
(r, s+d)
Joey drew DJKL with the coordinates (2, 3), (4, 3), and (5, 2). She reflected this triangle over the x-axis to create an image. What are the coordinates of the image?
(2, -3), (4, -3), and (5, -2)
Sue drew a triangle with coordinates (1, 3), (3, 2), and (4, 2). She drew an image of the triangle with coordinates (-1, 3), (-3, 2), and (-4, 2). How did she make the image?
Reflected over the y-axis
If triangeCAT ≅ triangleDOG, which statement must be true?
a. m∠A = m∠O
b. ∠C ≅ ∠G
c. CA = OG
d. CT ≅ DO
Jon drew a triangle with coordinates (5, 1), (7, -2) and (3, -1). He drew an image of the triangle with coordinates (1, 3), (3, 0), and (-1, 1). How did he make the image?
Left 4, up 2
Suppose (x,y) is moved to the right a units 2 times and then moved down b units 4 times. Write the coordinates of the image of the point. (Note: a and b are both positive integers).
(x+2a, y-4b)
Jon drew a triangle with coordinates (5, 1), (7, -2) and (3, -1). He drew an image of the triangle with coordinates (5, 1), (7, -2), and (3, -1) by completing a series of reflections. How did he make the image?
An even number of the same type of reflections (E.g. reflect over x-axis twice, over x-axis 4 times, etc.)
Suppose (x,y) is reflected across the x axis 2 times and then reflected across the y-axis 3 times. Write the coordinates of the image of the point.
(-x, y)
Jon drew a triangle with coordinates (5, 1), (7, -2) and (3, -1). He drew an image of the triangle with coordinates (4, -1), (6, 2), and (2, 1). How did he make the image?
Reflect over the x-axis and translate left 1.