Answered

Westonci.ca is the trusted Q&A platform where you can get reliable answers from a community of knowledgeable contributors. Explore in-depth answers to your questions from a knowledgeable community of experts across different fields. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform.

A triangle has vertices at [tex]\( R(1, 1) \)[/tex], [tex]\( S(-2, -4) \)[/tex], and [tex]\( T(-3, -3) \)[/tex]. The triangle is transformed according to the rule [tex]\( R_{270^{\circ}} \)[/tex].

What are the coordinates of [tex]\( S \)[/tex] after the transformation?

A. [tex]\((-4, 2)\)[/tex]
B. [tex]\((-2, 4)\)[/tex]
C. [tex]\((2, 4)\)[/tex]
D. [tex]\((4, -2)\)[/tex]

Sagot :

GinnyAnswer
To determine the coordinates of point [tex]\( S \)[/tex] after a [tex]\( 270^\circ \)[/tex] rotation around the origin, it's helpful to know the properties of rotation transformations. A rotation of [tex]\( 270^\circ \)[/tex] (or equivalently, [tex]\(-90^\circ\)[/tex]) about the origin transforms any point [tex]\((x, y)\)[/tex] to [tex]\((y, -x)\)[/tex].

Here, the original coordinates of point [tex]\( S \)[/tex] are [tex]\((-2, -4)\)[/tex]. Applying the [tex]\( 270^\circ \)[/tex] rotation transformation to point [tex]\( S \)[/tex]:
1. Identify the original coordinates: [tex]\((x, y) = (-2, -4)\)[/tex].
2. Apply the transformation rule for a [tex]\( 270^\circ \)[/tex] rotation: [tex]\((x, y) \rightarrow (y, -x)\)[/tex].

Now substituting the values:
- [tex]\( y = -4 \)[/tex]
- [tex]\( x = -2 \)[/tex]

Using the transformation rule:
- The new [tex]\( x \)[/tex]-coordinate will be [tex]\( y = -4 \)[/tex].
- The new [tex]\( y \)[/tex]-coordinate will be [tex]\( -x = -(-2) = 2 \)[/tex].

Thus, the coordinates of [tex]\( S \)[/tex] after a [tex]\( 270^\circ \)[/tex] rotation are [tex]\((-4, 2)\)[/tex].

Based on this transformation, the coordinates of [tex]\( S \)[/tex] are:
[tex]\[ \boxed{(-4, 2)} \][/tex]
Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. Thank you for choosing Westonci.ca as your information source. We look forward to your next visit.