Question

unit 1 end - of - unit assessment: rigid transformations
student instructions: you may use a straightedge, tracing paper, and your reference chart.
1.
(x,y)
a. draw triangle a after the translation (x,y)→(x + 1,y−2). label the new triangle b.
b. draw triangle a after it has been reflected over the y - axis. label the new triangle c.
c. draw triangle a after it has been rotated 90° clockwise about the origin. label the new triangle d.
d. draw triangle a after it has been reflected over the line y = - 2. label the new triangle e.

Explanation:

Step1: Translation rule application

For each vertex \((x,y)\) of triangle \(A\), use the rule \((x,y)\to(x + 1,y-2)\) to find the new - coordinates for triangle \(B\). For example, if a vertex of \(A\) is \((x_0,y_0)\), the corresponding vertex of \(B\) is \((x_0 + 1,y_0-2)\). Then plot the new triangle \(B\).

Step2: Reflection over y - axis rule

The rule for reflecting a point \((x,y)\) over the \(y\) - axis is \((x,y)\to(-x,y)\). Apply this rule to each vertex of triangle \(A\) to get the vertices of triangle \(C\). Then plot triangle \(C\).

Step3: 90 - degree clockwise rotation rule

The rule for rotating a point \((x,y)\) 90 degrees clockwise about the origin is \((x,y)\to(y,-x)\). Apply this rule to each vertex of triangle \(A\) to find the vertices of triangle \(D\). Then plot triangle \(D\).

Step4: Reflection over \(y=-2\) rule

To reflect a point \((x,y)\) over the line \(y =-2\), first find the distance \(d=y-(-2)=y + 2\) between the point and the line \(y=-2\). The new \(y\) - coordinate is \(y-2d=y-2(y + 2)=-y - 4\), and the \(x\) - coordinate remains the same. Apply this rule to each vertex of triangle \(A\) to get the vertices of triangle \(E\). Then plot triangle \(E\).

Since this is a drawing - based problem, a text - only response can't fully answer it. But the steps above explain how to perform each transformation to draw the required triangles. In a real - world scenario, you would use a straightedge and tracing paper as instructed in the problem to accurately draw the triangles on the given coordinate grids.

Answer:

You need to perform the above - described transformations on the given triangle \(A\) on the coordinate grids to draw triangles \(B\), \(C\), \(D\), and \(E\) respectively.