Geometry: Transformations (Middle School)
Practice translations, reflections, rotations, and dilations on the coordinate plane
Geometry: Transformations (Middle School)
Practice translations, reflections, rotations, and dilations on the coordinate plane
Geometry - Grade 6-8
- 1
Point A is located at (2, 3). Translate point A 4 units right and 2 units down. What are the coordinates of A'?
Right changes x in the positive direction, and down changes y in the negative direction.
The coordinates of A' are (6, 1). Moving 4 units right adds 4 to the x-coordinate, and moving 2 units down subtracts 2 from the y-coordinate. - 2
Triangle ABC has vertices A(1, 1), B(4, 1), and C(2, 3). Translate the triangle 3 units left and 5 units up. List the coordinates of A', B', and C'.
The translated coordinates are A'(-2, 6), B'(1, 6), and C'(-1, 8). Subtract 3 from each x-coordinate and add 5 to each y-coordinate. - 3
Reflect point P(-3, 5) across the x-axis. What are the coordinates of P'?
Across the x-axis means the point moves the same distance to the other side of the horizontal axis.
The coordinates of P' are (-3, -5). A reflection across the x-axis keeps the x-coordinate the same and changes the sign of the y-coordinate. - 4
Reflect point Q(6, -2) across the y-axis. What are the coordinates of Q'?
The coordinates of Q' are (-6, -2). A reflection across the y-axis changes the sign of the x-coordinate and keeps the y-coordinate the same. - 5
A point R is at (4, -7). Rotate R 90 degrees counterclockwise about the origin. What are the coordinates of R'?
For a 90 degree counterclockwise rotation, switch the coordinates and change the sign of the original y-coordinate.
The coordinates of R' are (7, 4). A 90 degree counterclockwise rotation about the origin follows the rule (x, y) becomes (-y, x). - 6
A point S is at (-2, 8). Rotate S 180 degrees about the origin. What are the coordinates of S'?
The coordinates of S' are (2, -8). A 180 degree rotation about the origin changes the sign of both coordinates. - 7
Rectangle WXYZ has vertices W(1, 2), X(5, 2), Y(5, 4), and Z(1, 4). Dilate the rectangle by a scale factor of 2 with the center of dilation at the origin. List the coordinates of W', X', Y', and Z'.
Multiply every x-coordinate and every y-coordinate by the scale factor.
The dilated coordinates are W'(2, 4), X'(10, 4), Y'(10, 8), and Z'(2, 8). A dilation by a scale factor of 2 from the origin multiplies each coordinate by 2. - 8
A triangle has side lengths 3 cm, 4 cm, and 5 cm. It is dilated by a scale factor of 3. What are the side lengths of the new triangle?
The new side lengths are 9 cm, 12 cm, and 15 cm. A dilation with scale factor 3 multiplies each side length by 3. - 9
Figure A is moved to Figure B by sliding every point 6 units to the right and 1 unit down. What type of transformation is this?
A slide is the common description of this transformation.
This transformation is a translation. A translation slides a figure without turning it, flipping it, or changing its size. - 10
A figure is flipped over a line so that each point and its image are the same distance from the line. What type of transformation is this?
This transformation is a reflection. A reflection flips a figure across a line called the line of reflection. - 11
The rule (x, y) becomes (x + 2, y - 4) is applied to a figure. Describe the transformation in words.
Look at how the x-coordinate and y-coordinate change separately.
The transformation is a translation 2 units right and 4 units down. Adding 2 to x moves the figure right, and subtracting 4 from y moves it down. - 12
The rule (x, y) becomes (-x, y) is applied to a figure. Identify the transformation.
The transformation is a reflection across the y-axis. The x-coordinate changes sign, and the y-coordinate stays the same. - 13
A shape is rotated 90 degrees clockwise about the origin. Point T(-5, 3) is on the shape. What are the coordinates of T'?
For a 90 degree clockwise rotation, switch the coordinates and change the sign of the original x-coordinate.
The coordinates of T' are (3, 5). A 90 degree clockwise rotation about the origin follows the rule (x, y) becomes (y, -x). - 14
A quadrilateral has vertices A(-1, 2), B(2, 2), C(3, -1), and D(-2, -1). Reflect the quadrilateral across the x-axis. List the coordinates of A', B', C', and D'.
The reflected coordinates are A'(-1, -2), B'(2, -2), C'(3, 1), and D'(-2, 1). A reflection across the x-axis changes the sign of each y-coordinate. - 15
A figure is transformed using the rule (x, y) becomes (0.5x, 0.5y). Is the image larger, smaller, or the same size as the original? Explain.
A scale factor less than 1 makes a figure shrink.
The image is smaller than the original. The rule is a dilation with scale factor 0.5, so all distances from the origin are half as large.