Two triangles are congruent if there is a way of writing a correspondence so that all of the corresponding sides and angles are
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<h2>DISCLAIMER: I think this is wrong, can somebody please flag it? I don't want others to get this wrong, sorry!!!</h2>Explanation:
- The question says: Mrs. Smith has a large grid drawn on a whiteboard at the front of her classroom. She and her geometry students use an erasable marker to plot shapes on it. She plots Triangle 1, which is shown on the grid below.
- Part A says: Mrs. Smith asks Marisa to transform Triangle 1 using the rule (x, y) --> (x + 2, y + 3) and then draw the resulting triangle (Triangle 2) on the whiteboard. Draw Triangle 2 on the grid below.
- Part B says: Next, Mrs. Smith asks another student, James, to write a rule that would reflect a figure across the line y = 3. She then asks him to transform Triangle 2 using this rule and draw the new triangle (Triangle 3) on the whiteboard. What is a rule that reflects a figure across the line y = 3? Draw Triangle 3 on the grid below.
- Part A is referring to the diagram that is provided with this question. It shows a triangle on a coordinate plane, and asks us to use the rule (x, y) --> (x + 2, y + 3). This is known as a translation in geometry (see Khan Academy for further details). The first part of the coordinate (x + 2) tells us that we should use the original x-value, and add 2. The second part of the coordinate (y + 3) tells us that we should use the original y-value, and add 3.
- So, now look at "Triangle 1" (see the image attached). This is the triangle given, so we can pick a random coordinate and follow the rule. If we pick (-4,-2), then we have to follow the rule by adding 2 to the x-value and 3 to the y-value. So, it would be (-4+2,-2+3).
- Simplifying this, we get (-2,1). As seen in the answer provided, this is the correct coordinate. Now that this coordinate is translated, we need to move the entire shape 2 to the right and 3 upwards. We can do this by continuing to follow the rule.
- Part B is referring to the diagram that is provided with this question. It shows an empty coordinate plane, and asks us to create a figure that will reflect across the equation y=3. This is known as a reflection in geometry (see Khan Academy for further details).
- First, we need to graph y = 3. So, now look at "Graph for y = 3" (see image attached). This is the line that our figure needs to be reflected across. When looking at this graph, we can see that the equation is parallel to the x-axis; therefore, the rule needs to be related to the x-axis.
- A common reflection rule that is used is the reflection of shapes across the x-axis, and this can be expressed as (x,y) --> (x,-y). Now that we have our rule, we just need to apply it to our figure. Our figure is the figure that we made in Part A. Let's pick a random coordinate and follow the rule. If we pick (-2,1), then we have to follow the rule by keeping the x-value the same and multiplying the y-value by -1. So, it would be (-2,1*-1).
- Simplifying this, we get (-2,-1). As seen in the answer provided, this is the correct coordinate. Now that this coordinate is reflected, we need to reflect the entire shape. We can do this by continuing to follow the rule.
