Question

3.04 translation practice assignment – geo a
print this document and do the work by hand, or save the
document and use the drawing tools to complete electronically.
translate/rotate each shape according to the rule on the
coordinate plane. label the new points appropriately as a’, b’,
c’, and d’.

1. translate the parallelogram by the rule: (x + 6, y – 2). then

rotate counterclockwise -270. plot all points and connect the
lines.
grid image with parallelogram vertices a, b, c, d
ordered pairs: a = ____ b = __ c = ____ d
= ______
ordered pairs: a’ = ____ b’ = __ c’ = ____ d’
= ______
ordered pairs: a’’ = ____ b’’ = __ c’’ = ____
d’’ = ______

Explanation:

Step1: Find Original Coordinates

Identify coordinates of A, B, C, D from graph.
A: \((-7, 3)\), B: \((-2, 3)\), C: \((-3, 1)\), D: \((-8, 1)\)

Step2: Apply Translation \((x + 6, y - 2)\)

For each point, add 6 to \(x\), subtract 2 from \(y\).
A': \((-7 + 6, 3 - 2) = (-1, 1)\)
B': \((-2 + 6, 3 - 2) = (4, 1)\)
C': \((-3 + 6, 1 - 2) = (3, -1)\)
D': \((-8 + 6, 1 - 2) = (-2, -1)\)

Step3: Apply Rotation \(-270^\circ\) (Counterclockwise)

Rotation rule: \((x, y) \to (y, -x)\) (since \(-270^\circ\) CCW is equivalent to \(90^\circ\) CW, or using rotation matrix for \(-270^\circ\): \((x, y) \to (y, -x)\)).
A'': \((1, -(-1)) = (1, 1)\) (Wait, correction: \(-270^\circ\) CCW rotation: the formula is \((x, y) \to (y, -x)\)? Wait, standard rotation: \(90^\circ\) CCW:[SSE Completed, Client Connection Error][LLM SSE On Failure]

Answer:

Step1: Find Original Coordinates

Identify coordinates of A, B, C, D from graph.
A: \((-7, 3)\), B: \((-2, 3)\), C: \((-3, 1)\), D: \((-8, 1)\)

Step2: Apply Translation \((x + 6, y - 2)\)

For each point, add 6 to \(x\), subtract 2 from \(y\).
A': \((-7 + 6, 3 - 2) = (-1, 1)\)
B': \((-2 + 6, 3 - 2) = (4, 1)\)
C': \((-3 + 6, 1 - 2) = (3, -1)\)
D': \((-8 + 6, 1 - 2) = (-2, -1)\)

Step3: Apply Rotation \(-270^\circ\) (Counterclockwise)

Rotation rule: \((x, y) \to (y, -x)\) (since \(-270^\circ\) CCW is equivalent to \(90^\circ\) CW, or using rotation matrix for \(-270^\circ\): \((x, y) \to (y, -x)\)).
A'': \((1, -(-1)) = (1, 1)\) (Wait, correction: \(-270^\circ\) CCW rotation: the formula is \((x, y) \to (y, -x)\)? Wait, standard rotation: \(90^\circ\) CCW:[SSE Completed, Client Connection Error][LLM SSE On Failure]