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A triangle has the coordinates [tex]$A(-16, -4)$[/tex], [tex]$B(2, 8)$[/tex], and [tex]$C(4, 6)$[/tex]. If the triangle is reflected about the [tex]$y$[/tex]-axis, what are the new coordinates for point [tex]$C$[/tex]?

A. [tex]$(-6, -4)$[/tex]
B. [tex]$(6, 4)$[/tex]
C. [tex]$(-4, 6)$[/tex]
D. [tex]$(4, -6)$[/tex]



Answer :

GinnyAnswer
To solve for the new coordinates of point [tex]\( C \)[/tex] after the triangle is reflected about the [tex]\( y \)[/tex]-axis, we need to understand the process of reflection over the [tex]\( y \)[/tex]-axis.

When a point [tex]\( (x, y) \)[/tex] is reflected about the [tex]\( y \)[/tex]-axis, the [tex]\( x \)[/tex]-coordinate changes its sign while the [tex]\( y \)[/tex]-coordinate remains unchanged.

Given the coordinates of point [tex]\( C \)[/tex] are [tex]\( (4, 6) \)[/tex], we reflect this point by changing the sign of the [tex]\( x \)[/tex]-coordinate:

1. Original point [tex]\( C \)[/tex]: [tex]\( (4, 6) \)[/tex]
2. Reflecting over the [tex]\( y \)[/tex]-axis:
- Change the [tex]\( x \)[/tex]-coordinate from [tex]\( 4 \)[/tex] to [tex]\( -4 \)[/tex]
- The [tex]\( y \)[/tex]-coordinate remains [tex]\( 6 \)[/tex]

Therefore, the new coordinates of point [tex]\( C \)[/tex] after the reflection are [tex]\( (-4, 6) \)[/tex].

So, the correct answer is:
[tex]\[ (-4, 6) \][/tex]

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