Question

unit 2 test lesson 21 to 28 total points 40 (v1)

1. given a rectangle blue with coordinates: b (2, 3), l (2, 6), u (8, 6) and e (8, 3). perform the following transformations in order.

part a - graph and label its image after a rotation of 180°. (5 points)
part b - translate the image from part a (x + 12, y - 4). graph and label its image b\l\u\e\. (5 points)
b____ b\____
l____ l\____
u____ u\____
e____ e\____

Explanation:

Step1: Rotation of 180°

The rule for a rotation of 180° about the origin is \((x,y)\to(-x,-y)\).
For point \(B(2,3)\): \(B'\) is \((- 2,-3)\)
For point \(L(2,6)\): \(L'\) is \((-2,-6)\)
For point \(U(8,6)\): \(U'\) is \((-8,-6)\)
For point \(E(8,3)\): \(E'\) is \((-8,-3)\)

Step2: Translation \((x + 12,y-4)\)

The rule for translation \((x,y)\to(x + 12,y-4)\)
For \(B'(-2,-3)\): \(B''=(-2+12,-3 - 4)=(10,-7)\)
For \(L'(-2,-6)\): \(L''=(-2+12,-6 - 4)=(10,-10)\)
For \(U'(-8,-6)\): \(U''=(-8+12,-6 - 4)=(4,-10)\)
For \(E'(-8,-3)\): \(E''=(-8+12,-3 - 4)=(4,-7)\)

Answer:

\(B'(-2,-3)\), \(B''(10,-7)\)
\(L'(-2,-6)\), \(L''(10,-10)\)
\(U'(-8,-6)\), \(U''(4,-10)\)
\(E'(-8,-3)\), \(E''(4,-7)\)