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To find the new coordinates of point [tex]\( T \)[/tex] after reflecting it through the [tex]\( x \)[/tex]-axis, we need to understand how reflections work with coordinates.
When a point [tex]\((x, y)\)[/tex] is reflected through the [tex]\( x \)[/tex]-axis, the [tex]\( x \)[/tex]-coordinate remains the same, while the [tex]\( y \)[/tex]-coordinate is inverted (multiplied by [tex]\(-1\)[/tex]). Let's apply this rule to point [tex]\( T \)[/tex].
The original coordinates of point [tex]\( T \)[/tex] are [tex]\((-11, -5)\)[/tex]. Reflecting this point through the [tex]\( x \)[/tex]-axis involves the following steps:
1. Keep the [tex]\( x \)[/tex]-coordinate the same: [tex]\(-11\)[/tex].
2. Invert the [tex]\( y \)[/tex]-coordinate: [tex]\(-5\)[/tex] becomes [tex]\(5\)[/tex].
Therefore, after reflecting point [tex]\( T \)[/tex] through the [tex]\( x \)[/tex]-axis, the new coordinates will be:
[tex]\[ (-11, 5) \][/tex]
Thus, the new coordinates of point [tex]\( T \)[/tex] are [tex]\((-11, 5)\)[/tex].
The correct answer is [tex]\((-11, 5)\)[/tex].
When a point [tex]\((x, y)\)[/tex] is reflected through the [tex]\( x \)[/tex]-axis, the [tex]\( x \)[/tex]-coordinate remains the same, while the [tex]\( y \)[/tex]-coordinate is inverted (multiplied by [tex]\(-1\)[/tex]). Let's apply this rule to point [tex]\( T \)[/tex].
The original coordinates of point [tex]\( T \)[/tex] are [tex]\((-11, -5)\)[/tex]. Reflecting this point through the [tex]\( x \)[/tex]-axis involves the following steps:
1. Keep the [tex]\( x \)[/tex]-coordinate the same: [tex]\(-11\)[/tex].
2. Invert the [tex]\( y \)[/tex]-coordinate: [tex]\(-5\)[/tex] becomes [tex]\(5\)[/tex].
Therefore, after reflecting point [tex]\( T \)[/tex] through the [tex]\( x \)[/tex]-axis, the new coordinates will be:
[tex]\[ (-11, 5) \][/tex]
Thus, the new coordinates of point [tex]\( T \)[/tex] are [tex]\((-11, 5)\)[/tex].
The correct answer is [tex]\((-11, 5)\)[/tex].
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