![]() The sign of the image’s \(y\)-coordinate is opposite the original, so the image is on the opposite sign of the axis as the original.The \(y\)-coordinates of the original and image points have the same absolute value, so the distance from the \(x\)-axis is the same for each.Consider displaying an image of the solution and drawing segments that connect pairs of original and image points. Why does this rule produce a reflection?” Guide students through the different aspects of the geometric definition of a reflection. Look at the definition of a reflection on your reference chart. Now ask students, “The rule \((x,y) \rightarrow (x, \text-y)\) is a reflection across the \(x\)-axis. A translation is a rigid motion-it produces a result that does not change size or shape.) “Can we call \((x,y)\rightarrow (2x,y)\) a translation? Why or why not?” (No.Also, in this example we can see that the angles of the dilated figure are not congruent to the angles in the original.) In a dilation, the figure is stretched in all directions by the same factor, not just 1 direction. “Can we call \((x,y)\rightarrow (2x,y)\) a dilation? Why or why not?” (No.The second rule just had the \(x\)-coordinate multiplied by 2. It is stretched both vertically and horizontally by the same factor. Compare and contrast these rules.” (In the first rule, both coordinates were multiplied by 2. In this activity, one rule was \((x,y)\rightarrow (2x,y)\). “In the previous activity, one rule was \((x,y)\rightarrow (2x,2y)\).The goal of the discussion is to make connections between the coordinate rules and the geometric descriptions of transformations. The result is \((\text-3,\text-2)\), or the transformation of rotating \(A\) 180 degrees using the origin as a center.) Which transformation from above could this represent, and why? (It is telling us to multiply each coordinate by -1. Now ask students to consider this notation: \((x,y) \rightarrow (\text-x,\text-y)\). This can be read aloud as “the transformation that takes point \((x,y)\) to \((x-4,y)\).” Which transformation from the warm-up could this represent, and why? (It is telling us to subtract 4 units from the \(x\)-coordinate. So far we have written the rules out in sentences, but when we are working in the coordinate plane there is notation we can use as shorthand.Īsk students to consider this notation: \((x,y) \rightarrow (x-4,y)\). “Who can restate \(\underline\)’s strategy?”Īfter students have discussed each problem, tell them that transformation rules can be viewed as functions which take a point in the plane as an input and give another point in the plane as an output. ![]() To involve more students in the conversation, consider asking: Record and display their responses for all to see. Ask students to share their strategies for each problem. ![]()
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