![]() ![]() Doing so gives us the following.(x,y)\rightarrow (−x,−y)\). □ ′ ( − 1, 3 ), and □ ′ ( − 1, 1 ), we can plot them on the set Now that we have found the coordinates of the vertices of the image, □ ′ ( − 4, 2 ), So, the coordinates of □ ′ are ( − 1, 1 ). This then gives us the coordinates ( − 4, 2 ), so the coordinates ofįor □ ( 3, 1 ), we let □ = 3 and □ = 1. See that the □-coordinate and □-coordinate have switched places and that there is a change Substituting this into ( − □, □ ), we can We let □ = 2 and □ = 4 (since they are the □-coordinate and Having found the vertices, we can then apply the rule for the geometric transformation ( □, □ ) → ( − □, □ ) to each set of coordinates to find the coordinates of the image.įor □ ( 2, 4 ), to use the rule ( □, □ ) → ( − □, □ ), Of the single transformations rotation was the most difficult and translations were the easiest. Reflections involve flipping an object over a line. MY REFLECTIONS (over line l) There is a lot in this objective (1) Performing single transformations (2) Developing the rules for those transformations and then (3) Performing sequences of transformations. □ ( 1, 2 ), the top-right vertex at □ ( 2, 2 ), and the bottom-right vertex at There are four main types of transformations: Rotations involve turning an object around a point. Have edges of length one unit, with the bottom-left vertex at □ ( 1, 1 ), the top-left vertex at To make working out coordinates easier, we will choose vertices that Need to make sure each of the sides are the same length and at 90 degrees Since we are not told any vertices, let’s consider a specific example by choosing vertices ourselves. We are told that the vertices of a square are transformed by the transformation ( □, □ ) → ( − □, □ ) therefore, in order to help us work out which transformation has taken place, it is helpful toĪssign coordinates to the vertices of the square. Which of the following geometric transformations is performed? The vertices of a square are transformed by the transformation ( □, □ ) → ( − □, □ ). Measure the same distance again on the other side and place a dot. ![]() △ □ □ □, which are □ ( 1, 3 ), □ ( 3, 3 ),Įxample 4: Identifying the Type of a Transformation given Its Rule Measure from the point to the mirror line (must hit the mirror line at a right angle) 2. Taking our previous example, we can demonstrate what transformation has taken place on △ □ □ □īy plotting its coordinates and the coordinates of its image. ![]() Therefore, the vertices of the image have coordinates □ ′ ( 1, − 3 ), □ ′ ( 3, − 3 ), and To find out which of the options given represents the image of △ □ □ □, we substitute theĬoordinates of each of the vertices of △ □ □ □ into ( □, □ ) → ( □, − □ ) to give us the vertices of the image. Which of the following represents the image of △ □ □ □, where Position, as seen with the arrows on the diagram below.Įxample 3: Transforming a Shape Using Its Coordinates Third, we can see that the object and the image are the same size and orientation, with the only thing changing being the We therefore need to consider the orientation. This means that it is unlikely to be a rotation, Similarly, the bottom-right vertex in the object is □, and theīottom-right vertex in the image is □ ′, and so on. In other words, the bottom-left vertex in the object is □, and the bottom-left vertex in Second, we can see that the vertices of the object occur in the same relative positions to one another as the vertices This means that it cannot be a reflection otherwise, The first quadrilateral has vertices □ □ □ □ and the image has vertices □ ′ □ ′ □ ′ □ ′ in the same order counterclockwise. Remained the same and which have been changed.įirst, we can see that the vertices of the object occur in the same order as the vertices in the image. Reflection across the x-axis followed by a. To determine the type of transformation, we will consider which of the properties of both the object and the image have Reflection across the line y x followed by a translation by the vector <-1, 2> A.![]()
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