Answered

Points [tex]\(R, S\)[/tex], and [tex]\(T\)[/tex] have the coordinates [tex]\(R(10,7), S(22,1)\)[/tex], and [tex]\(T(-11,-5)\)[/tex]. Together the points make a triangle.

If the triangle is reflected through the [tex]\(x\)[/tex]-axis, which of the following would be the new coordinates of the point [tex]\(T\)[/tex]?

A. [tex]\((-11, 5)\)[/tex]

B. [tex]\((-11, -5)\)[/tex]

C. [tex]\((11, 5)\)[/tex]

D. [tex]\((11, -5)\)[/tex]



Answer :

GinnyAnswer
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].