![]() ![]() ![]() the triangle with vertices a(-1, -3), b(-4, -1), and c(-6, -4) is translated by the rule (x, y) → (x + 10, y) and then reflected over the x-axis. abcd → fehg by a reflection in the y-axis.Įxample 4. the rule (x, y) → (x + 4, y) maps point b and c only, it does not apply to the entire figure. in order for the rule to be correct, it would have to map all points on the preimage by the same translation vector. if not, identify the correct transformation.Ī. does abcd → fehg (x, y) → (x + 4, y)? if yes, explain how you know. Part d: is the transformation an isometry? solution: yes, there is no constant multiplied by the x coordinate or the y coordinate so the transformation is an isometry.Įxample 3. solution: the image of d is already known, set up an equation for x and an equation for y and solve: Part c: determine the preimage d for d′ (1, 7). solution: add 5 to the x-coordinate and add 2 to the y-coordinate: q(1, 6) → q′(1 + 5, 6 + 2) = (6, 8) solution: add 5 to the x-coordinate and add 2 to the y-coordinate: a(2, 3) → a′(2 + 5, 3 + 2) = (7, 5) use the transformation rule (x, y) → (x + 5, y + 2) to answer the following question. each point on the preimage is moved 3 units to the left and 4 units down. Solution: the drawing below shows the translation vectors for two pairs of corresponding vertices. describe the translation that maps the blue figure onto the red figure. to perform a composition of transformations, apply the rules one at a time.įor instance, if the point (2, 3) is reflected in the x-axis and then translated by the rule (x, y) → (x – 1, y – 3), first apply the rule for a reflection in the x-axis, and then apply the translation rule. The rules for different transformations are summarized here. the transformation of two or more isometries is also an isometry. When two or more transformations are combined to produce a single transformation, the result is called a composition of the transformations. The size of the preimage is not preserved. multiply each x-coordinate of the preimage by 2 and subtract 3, and multiply each y-coordinate of the preimage by 2. ![]() If the same preimage with endpoints (-2, 1) and (3, 4) is transformed according to the rule (x, y) → (2x – 3, 2y), the image will not be the same size as its preimage. the preimage is shifted 2 units to the right and 1 unit down, without changing its size or shape. The preimage is shown in blue and the image is shown in red. to translate the line segment by the rule (x + 2, y – 1), add 2 to both x coordinates and subtract 1 from both y coordinates. ![]() for example, consider the line segment with endpoints (-2, 1) and (3, 4). the multiplier changes the size of the image making it a non-rigid transformation. however, if the rule contains a constant multiplied by x or y, the transformation is no longer a translation. Such translations are isometries and shift the preimage without changing its size. for instance, in the coordinate plane below the translation (x, y) → (x + 4, y – 2) shifts each point 4 units to the right and 2 units down. this is a shift a units in the x-direction (horizontally) and b units in the y-direction (vertically). Often, the rule for the translation will be given as (x, y) → (x + a, y + b). a translation is an isometry, so the image of a translated figure is congruent to the preimage. a vector is a quantity that has both length and direction, and can be thought of as a line segment with a starting point and an endpoint. the distance and direction are indicated by a ray sometimes called the translation vector. solutionĮssential question: how can the coordinate plane help me understand properties of reflections, translations and rotations? lessonĪ translation is a transformation where all points of the figure are moved the same distance in the same direction. rotate the figure with vertices a(3, 3), b(2, 6) and c(-1, 1) 90º counter-clockwise about the origin. ![]()
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |