Question

geometry
describe the transformation that occurred as specifically as possible.
reflect the given shape over the y - axis. be sure to label the new points and state the ordered pairs.
b ____
h ____
t ____
expressions and equations
match each expression in the left column with an equivalent expression in the right column. explain how you know.
a. n + n + n + n
b. 4n - 36
c. n(9 - 4)
d. 4(n - 36)

1. (n - 36)·4
2. 4n+-9
3. 4n
4. 9n - 4n

Explanation:

Part 1: Describe the transformation

Step1: Observe the orientation change

The original triangle and the new - triangle have opposite orientations. Also, corresponding points are at the same distance from the y - axis. This indicates a reflection.
The transformation is a reflection over the y - axis.

Part 2: Reflect the given shape over the y - axis

Let's assume the coordinates of the points:
Suppose \(B=(x_1,y_1)\), \(H=(x_2,y_2)\), \(T=(x_3,y_3)\)
The rule for reflecting a point \((x,y)\) over the y - axis is \((x,y)\to(-x,y)\)
If \(B\) has coordinates \((- 4,0)\), then \(B'=(4,0)\)
If \(H\) has coordinates \((-4,3)\), then \(H'=(4,3)\)
If \(T\) has coordinates \((-2,5)\), then \(T'=(2,5)\)

Part 3: Match the expressions

Step1: Simplify expression A

\(n + n + n + n=4n\), so \(A\) matches \(3\)

Step2: Simplify expression B

\(4n-36\) does not match any of the right - hand side expressions exactly as they are written.

Step3: Simplify expression C

\(n(9 - 4)=n\times5 = 5n\), and \(9n-4n = 5n\), so \(C\) matches \(4\)

Step4: Simplify expression D

\(4(n - 36)=4n-144\), and \((n - 36)\times4=4n-144\), so \(D\) matches \(1\)

Answer:

• Transformation: Reflection over the y - axis
• \(B'=(4,0)\)
• \(H'=(4,3)\)
• \(T'=(2,5)\)
• \(A - 3\)
• \(B - \text{No match}\)
• \(C - 4\)
• \(D - 1\)