Point A (4,2) is reflected about the y-axis to Point B. Point B is then reflected about the line y=x to Point C. What are the coordinates of Point C?

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Point C is located at (2,-4).

We are given Point A with coordinates (4,2).

Point B is the image of the reflection of A over the y-axis. Algebraically the reflection of a point over the y-axis can be written as

`R_y(x,y)=(-x,y).`

The image point has the same y-coordinate as the...

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Point C is located at (2,-4).

We are given Point A with coordinates (4,2).

Point B is the image of the reflection of A over the y-axis. Algebraically the reflection of a point over the y-axis can be written as

`R_y(x,y)=(-x,y).`

The image point has the same y-coordinate as the preimage, while the x-coordinate is opposite in sign.

So B is located at (-4,2).

Another way to see this is that the image of a point reflected about a line is on the line through the preimage perpendicular to the line of reflection and equidistant from the line of reflection. We see that y=2 is the line that contains (4,2) and is perpendicular to the y-axis. As (4,2) is 4 units from the axis, its image will be 4 units in the opposite direction.

C is the image of B reflected over the line y=x.

Algebraically we have `R_(y=x)(x,y)=(y,x).` The image point exchanges the x and y coordinates.

Thus C is at (2,-4).

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