Question

answer a and b for each of the transformations below. a) identify the two transformations that occurred. b) write a similarity or congruency statement for the pre - image and image. 25. 26. 27.

Explanation:

Step1: Analyze transformation in 25a

By observing the position of the rectangle, it is translated (shifted) vertically upwards. Let's assume the coordinates of a vertex of the pre - image rectangle \(WXYZ\) and its corresponding vertex in the image rectangle \(W'X'Y'Z'\). If we consider the \(y\) - coordinates of corresponding points, the \(y\) - value of each point in the image is greater than that of the pre - image.

Step2: Write congruency statement for 25a

Since translation is a rigid transformation (preserves shape and size), the pre - image rectangle \(WXYZ\) and the image rectangle \(W'X'Y'Z'\) are congruent. The congruency statement is \(\text{WXYZ}\cong\text{W'X'Y'Z'}\).

Step3: Analyze transformation in 26a

The triangle \(DEF\) is reflected across the \(y\) - axis. We can check the \(x\) - coordinates of corresponding points. For a point \((x,y)\) in \(\triangle DEF\), its corresponding point in \(\triangle D'E'F'\) has coordinates \((-x,y)\).

Step4: Write congruency statement for 26a

Reflection is a rigid transformation, so \(\triangle DEF\cong\triangle D'E'F'\).

Step5: Analyze transformation in 27a

The triangle \(PQR\) is rotated \(90^{\circ}\) counter - clockwise about the origin. We can use the rule for a \(90^{\circ}\) counter - clockwise rotation \((x,y)\to(-y,x)\) to check the coordinates of corresponding points.

Step6: Write congruency statement for 27a

Rotation is a rigid transformation, so \(\triangle PQR\cong\triangle P'Q'R'\).

Answer:

25a: Translation, \(\text{WXYZ}\cong\text{W'X'Y'Z'}\)
26a: Reflection across the \(y\) - axis, \(\triangle DEF\cong\triangle D'E'F'\)
27a: \(90^{\circ}\) counter - clockwise rotation about the origin, \(\triangle PQR\cong\triangle P'Q'R'\)