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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]\( R_{0,270^{\circ}} \)[/tex]. What are the coordinates of [tex]\( S' \)[/tex]?

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



Answer :

GinnyAnswer
Let's begin by understanding the transformation rule [tex]\( R_{0,270^{\circ}} \)[/tex]. This rule indicates a rotation of 270 degrees counterclockwise about the origin.

For a point [tex]\((x, y)\)[/tex], rotating it 270 degrees counterclockwise about the origin means transforming it in such a way that its new coordinates [tex]\((x', y')\)[/tex] are given by:
[tex]\[ x' = y \][/tex]
[tex]\[ y' = -x \][/tex]

We need to apply this transformation to the coordinates of point [tex]\(S\)[/tex], which are [tex]\((-2, -4)\)[/tex].

Following the rules of transformation:

1. Assign [tex]\( x = -2 \)[/tex] and [tex]\( y = -4 \)[/tex].
2. Calculate the new x-coordinate [tex]\(x'\)[/tex]:
[tex]\[ x' = y = -4 \][/tex]

3. Calculate the new y-coordinate [tex]\(y'\)[/tex]:
[tex]\[ y' = -x = -(-2) = 2 \][/tex]

Therefore, the coordinates of [tex]\(S'\)[/tex] after a 270-degree counterclockwise rotation about the origin are [tex]\((-4, 2)\)[/tex].

The correct answer is:
[tex]\[ (-4, 2) \][/tex]

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