Translations & Rotations
Reflections & Rotations
Algebraic Directions
100

If point A is at (2,2) and you translate it left 5 units, and up 2 units what would the point at A' be?

(-3,4)

100
If point A is located at (5,6) and it is reflected across the x-axis, what would point A' be?
(5,-6)
100
If you have point (x,y) and you are asked to move the point a units to the right and b units down, what would your new point be?
(x+a,y-b)
200

What is the inverse of L:(x,y)-->(x-2, y+3)

L:(x,y)-->(x+2, y-3)

200

If you have point G at (-3,2) and you rotate it 90 degrees clockwise, what would the point G' be?

(2,3)

200
If you have point (x,y) and you are asked to reflect it over the x-axis, what would your new point be?
(x,-y)
300

If point J is at (3,-4) and you translate it left 5 units & up 5/2 units, what would the point at J' be?

(-2,-1.5)

300

Given point R(-2z - 1, 3t).  If R'(4, -5) after reflecting it across the line y=x, find the z and t

t = 4/3, z=2

300
If you have point (x,y) and you are asked to rotate it 180 degrees, what would your new point be?
(-x,-y)
400

If point W is at (-5,0) and first you translate it right 7 units & up 3 units then you translate it left 2 units & down 3 units, what would the point at W' be?

(0,0) or the origin

400
If point K is located at (-2,-4) and it is reflected across the y-axis then reflected across the x-axis, what point would K' have?
(2,4)
400
If you had point (x,y) and you were asked to rotate it clockwise 90 degrees, what would your new point be?
(y,-x)
500
If you have point Q at (1,-4) and it is translated left 3 units & up 5 units then it is reflected across the y-axis and finally rotated 180 degrees, what point would Q' be?
(-2,-1)
500
If point X is located at (-5,-5) and it is translated 8 units to the right and 2 units up then it is reflected across the y-axis, what would the point for X' be?
(-3,-3)
500

Write the steps to reflect (x,y) across the line y=mx+b

1. Find a line perpendicular to y=mx+b that goes through (x,y) - (remember: perpendicular is the opposite reciprocal slope)

2. Find the point of intersection of the two lines

3. Find the other endpoint of the line with the point of intersection and (x,y) using the midpoint formula

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