Question 1 (Essay Worth 10 points) (02.03 MC)

Figure ABCD is transformed to obtain figure A'B'C'D':

A coordinate grid is shown from negative 6 to 6 on both axes at increments of 1. Figure ABCD has A at ordered pair negative 4, 4, B at negative 2, 2, C at negative 2, negative 1, D at negative 4, 1. Figure A prime B prime C prime D prime has A prime at ordered pair 3, negative 4, B prime at 5, negative 2, C prime at 5, 1, D prime at 3, negative 1.

Part A: Write the sequence of transformations that changes figure ABCD to figure A'B'C'D'. Explain your answer and write the coordinates of the figure obtained after each transformation. (6 points)

Part B: Are the two figures congruent? Explain your answer. (4 points)

Question 2 (Essay Worth 10 points)
(02.05 MC)

Triangle PQR is transformed to triangle P'Q'R'. Triangle PQR has vertices P(4, 0), Q(0, −4), and R(−8, −4). Triangle P'Q'R' has vertices P'(1, 0), Q'(0, −1), and R'(−2, −1).

Plot triangles PQR and P'Q'R' on your own coordinate grid.

Part A: What is the scale factor of the dilation that transforms triangle PQR to triangle P'Q'R'? Explain your answer. (4 points)

Part B: Write the coordinates of triangle P"Q"R" obtained after P'Q'R' is reflected about the y-axis. (4 points)

Part C: Are the two triangles PQR and P''Q''R'' congruent? Explain your answer. (2 points)

Question 3 (Essay Worth 10 points)
(02.06 MC)

In the figure shown, line AB is parallel to line CD.

Part A: What is the measure of angle x? Show your work. (5 points)

Part B: Explain how you found the measure of angle x by identifying the angle relationships that you used along the transversal. (5 points)

AB and CD are parallel lines, and PQ and PR are transversals which intersect AB at P and CD at Q and R. Angle APQ is labeled as 62 degrees, angle QPR is equal to x, angle PRD is equal to 115 degrees.

Question 4 (Essay Worth 10 points)
(02.07 MC)

The figure shows triangle PQR and line segment AB, which is parallel to QR:

Triangle PQR has a point A on side PQ and point B on side PR. The line AB is parallel to the line QR.

Part A: Is triangle PQR similar to triangle PAB? Explain using what you know about triangle similarity. (5 points)

Part B: Which line segment on triangle PAB corresponds to line segment QR? Explain your answer. (3 points)

Part C: Which angle on triangle PAB corresponds to angle Q? Explain your answer. (2 points)