Reflection, Rotation & Translation Review
When you have a reflection over the y axis, what happens to the coordinates?
(x, y) → (-x, y) For example if the coordinates of point F are (2, 7); the coordinates of point F' (-2, 7) since the x coordinate would change their sign but the y coordinate will have the the same sign as the original coordinates.
When you have a reflection over the x axis, what happens to the coordinates?
(x, y) → (x, -y) For example if the coordinates of point C are (6, 8); the coordinates of point C' (6, -8) since the x coordinate would stay the same but the y coordinate will have the opposite sign.
transformation
A change in the position of a figure such as a reflection, rotation and translation
Reflection
A figure is FLIPPED onto a congruent image
Rotation
A figure is TURNED so that each point stays an equal distance from a single point
Translation
A figure is moved along a straight line without turning or flipping, SLIDE
Answer: J' (-6, 10) The reflected point will have the same coordinates for x and the opposite coordinates for y, since the point was reflected across the x axis.
A point J has the coordinates ( -6, -10). What are its new coordinates after reflecting point J across the x-axis?
Answer: W' (2, -3) The reflected point will have the same coordinates for y and the opposite coordinates for x, since the point was reflected across the y axis.
A point W with coordinates (-2, -3) is reflected across the y axis. What are its new coordinates?
Answer A' (-2,4) When you rotate a point or shape 90° CCW about the origin, the rule is (x,y) → (-y, x). Therefore A(4,2) moves to A'(-2,4).
Find A' after Triangle ABC is rotated 90° CCW about the origin, if A(4,2) B( 8,2) and C(6,5).
Answer E' (3, 2) When you reflect a point over the y axis the y coordinate will stay the same and the x coordinate will be the opposite. So E (-3, 2) → E¹( 3, 2)
Find E' in a reflection of Triangle MEG when M (1, 3), E( -3, 2), and G (-1, -2) over the y axis.
Answer Q' (5,3) When you rotate a point or shape 180° about the origin, the rule is (x,y)→(-x,-y), so the original coordinates for x and y become their opposites.
If Triangle PQR is rotated 180° about the origin, what is the coordinate of Q', if P(-4,-6) Q(-5,-3) and R(-1,-7).
Answer: C' C' is the correct way to refer to a duplicate image.
If the original point is point C then the new image would be
Answer: (-9, 4) When reflecting an image over the y axis the y coordinate will stay the same and the x coordinate will be the opposite value.
What is the image of (9, 4) if it is reflected over the y axis?
Answer: (12, 3) Take the original point of (9, 7) and apply the translation rule of right 3 down 4. (x, y) → (x +3, y-4) (9, 7)→ ( 9 + 3, 7-4)
What point is the image of ( 9, 7) with a translation of right 3 and down 4?
Answer: (x, y) → (x -4, y -3) Take the coordinates of the original point M (5, -8) and look at what you will need to do to those coordinates to create the new point M¹ ( 1, -11). Think if I start with 5 and end with 1 what did I do? Subtract 4. Then if I start with -8 and end with -11 what did I do? Subtract 3. So to get the new image I will subtract 4 from x and subtract 3 from y (x-4, y-3)
Write the rule using arrow notation for the translation of point M ( 5, -8) to point M' ( 1, -11).