Answered

Welcome to Westonci.ca, the place where your questions find answers from a community of knowledgeable experts. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately. Experience the convenience of finding accurate answers to your questions from knowledgeable experts on our platform.

A triangle has vertices at [tex]\(L(2,2), M(4,4),\)[/tex] and [tex]\(N(1,6)\)[/tex]. The triangle is transformed according to the rule [tex]\(R_0, 180^{\circ}\)[/tex].

Which statements are true regarding the transformation? Select three options.

A. The rule for the transformation is [tex]\((x, y) \rightarrow (-x, -y)\)[/tex].
B. The coordinates of [tex]\(L'\)[/tex] are [tex]\((-2, -2)\)[/tex].
C. The coordinates of [tex]\(M'\)[/tex] are [tex]\((-4, -4)\)[/tex].
D. The coordinates of [tex]\(N'\)[/tex] are [tex]\((6, -1)\)[/tex].
E. The coordinates of [tex]\(N'\)[/tex] are [tex]\((-1, -6)\)[/tex].

Sagot :

GinnyAnswer
Let's approach this step-by-step:

1. Understand the Transformation:
- The rule mentioned for the transformation is a [tex]$180^\circ$[/tex] rotation. In a [tex]$180^\circ$[/tex] rotation around the origin, each point [tex]\((x, y)\)[/tex] transforms to [tex]\((-x, -y)\)[/tex].

2. Apply the Transformation to Each Vertex:
- Vertex [tex]\(L\)[/tex]:
- Original coordinates: [tex]\(L(2, 2)\)[/tex]
- After transformation: [tex]\(L' = (-2, -2)\)[/tex]
- Vertex [tex]\(M\)[/tex]:
- Original coordinates: [tex]\(M(4, 4)\)[/tex]
- After transformation: [tex]\(M' = (-4, -4)\)[/tex]
- Vertex [tex]\(N\)[/tex]:
- Original coordinates: [tex]\(N(1, 6)\)[/tex]
- After transformation: [tex]\(N' = (-1, -6)\)[/tex]

3. Verify the Statements:
- Statement 1: "The rule for the transformation is [tex]\((x, y) \rightarrow (-x, -y)\)[/tex]"
- This is true since a [tex]$180^\circ$[/tex] rotation does indeed map each [tex]\((x, y)\)[/tex] to [tex]\((-x, -y)\)[/tex].

- Statement 2: "The coordinates of [tex]\(L'\)[/tex] are [tex]\((-2, -2)\)[/tex]"
- This is true based on the transformation of vertex [tex]\(L\)[/tex].

- Statement 3: "The coordinates of [tex]\(M'\)[/tex] are [tex]\((-4, 4)\)[/tex]"
- This is false. The correct coordinates of [tex]\(M'\)[/tex] are [tex]\((-4, -4)\)[/tex].

- Statement 4: "The coordinates of [tex]\(N'\)[/tex] are [tex]\((6, -1)\)[/tex]"
- This is false. The correct coordinates of [tex]\(N'\)[/tex] are [tex]\((-1, -6)\)[/tex].

- Statement 5: "The coordinates of [tex]\(N'\)[/tex] are [tex]\((-1, -6)\)[/tex]"
- This is true based on the transformation of vertex [tex]\(N\)[/tex].

Conclusion:
The three true statements regarding the transformation are:
1. The rule for the transformation is [tex]\((x, y) \rightarrow(-x, -y)\)[/tex].
2. The coordinates of [tex]\(L'\)[/tex] are [tex]\((-2, -2)\)[/tex].
5. The coordinates of [tex]\(N'\)[/tex] are [tex]\((-1, -6)\)[/tex].
Thank you for choosing our service. We're dedicated to providing the best answers for all your questions. Visit us again. We appreciate your time. Please come back anytime for the latest information and answers to your questions. We're dedicated to helping you find the answers you need at Westonci.ca. Don't hesitate to return for more.