Question

transformation: translation
______ 9. using the preimage below, which graph represents the image translated as ((x,y) \to (x - 3,y - 2))?

transformation: reflection
______ 10. using the preimage with vertices (j(-5, 4)), (k(-2, 5)), and (l(0, 3)), which graph represents the image reflected across (x)-axis?
reflection across the (x)-axis

Explanation:

Question 9 (Translation)

Step1: Identify Preimage Coordinates

First, find the coordinates of the preimage vertices \( D \), \( E \), \( F \). From the graph:

• \( D \): Let's assume \( D \) is at \( ( - 2, 1) \) (since it's on the grid, adjusting for the axes), \( F \) at \( (3, 1) \), \( E \) at \( (1, 4) \) (approximate, but the key is the translation rule \( (x,y) \to (x - 3,y - 2) \)).

Step2: Apply Translation Rule

For each vertex:

• \( D(-2,1) \to (-2 - 3,1 - 2)=(-5,-1) \)
• \( F(3,1) \to (3 - 3,1 - 2)=(0,-1) \)
• \( E(1,4) \to (1 - 3,4 - 2)=(-2,2) \)

Now, check the options. Option A has vertices that match this translation (moved left 3, down 2).

Question 10 (Reflection over x - axis)

Step1: Recall Reflection Rule

The rule for reflecting a point \( (x,y) \) over the \( x \) - axis is \( (x,y)\to(x, - y) \).

Step2: Apply Rule to Each Vertex

• For \( J(-5,4) \): Reflect to \( J'(-5,-4) \)
• For \( K(-2,5) \): Reflect to \( K'(-2,-5) \)
• For \( L(0,3) \): Reflect to \( L'(0,-3) \)

Now, check the options. Option B has vertices with \( y \) - coordinates negated, matching the reflection over the \( x \) - axis.

Answer:

(Question 9)
A