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.
coordinate plane image with a parallelogram labeled a, b, c, d
ordered pairs: a = ____ b = __ c = ____ d
= ______
ordered pairs: a’ = ____ b’ = __ c’ = ____ d’
= ______
ordered pairs: a’’ = ____ b’’ = __ c’’ = ____
d’’ = ______

Explanation:

Step1: Identify Original Coordinates

First, find the coordinates of points A, B, C, D from the graph.

• A: (-7, 3) (since it's 7 units left on x, 3 up on y)
• B: (-2, 3) (2 units left on x, 3 up on y)
• C: (-3, 1) (3 units left on x, 1 up on y)
• D: (-8, 1) (8 units left on x, 1 up on y)

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

For each point, add 6 to x-coordinate and subtract 2 from y-coordinate.

• \(A'\): \((-7 + 6, 3 - 2) = (-1, 1)\)
• \(B'\): \((-2 + 6, 3 - 2) = (4, 1)\)
• \(C'\): \((-3 + 6, 1 - 2) = (3, -1)\)
• \(D'\): \((-8 + 6, 1 - 2) = (-2, -1)\)

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

The rotation rule for \(-270^\circ\) (or equivalently \(90^\circ\) clockwise) is \((x, y) \to (y, -x)\).

• For \(A'(-1, 1)\): \(A'' = (1, -(-1)) = (1, 1)\)
• For \(B'(4, 1)\): \(B'' = (1, -4)\)
• For \(C'(3, -1)\): \(C'' = (-1, -3)\)
• For \(D'(-2, -1)\): \(D'' = (-1, -(-2)) = (-1, 2)\)

Answer:

Original Coordinates:
A = \((-7, 3)\), B = \((-2, 3)\), C = \((-3, 1)\), D = \((-8, 1)\)

After Translation:
A' = \((-1, 1)\), B' = \((4, 1)\), C' = \((3, -1)\), D' = \((-2, -1)\)

After Rotation:
A'' = \((1, 1)\), B'' = \((1, -4)\), C'' = \((-1, -3)\), D'' = \((-1, 2)\)