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The point (4, 3) is reflected in the x-axis. What is the image of this point?

The point (-3, -8) is reflected in the y-axis. What is the image of this point?

The point (2, 4) is reflected in the line x = -3. What is the image of this point?

The point (a, b) is reflected in the line y = x. What is the image of this point?

ΔXYZ is defined by its vertices X(1,3), Y(-3,5), and Z(0, -5). ΔXYZ is reflected in
the y-axis. What are the coordinates of its image X’Y’Z’?

The translation T: (x, y) → (x -2, y + 4) maps the point (2, -3) to

The translation T: (x, y) → (x + 3, y - 2) maps the point (-4, -3) to

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1 Answer

The point (4,3) reflected about the x axis,
=> The x remains the same, the y flips over the x axis to be negative
      (4,3) ==>> (4,-3)
 
The point (-3,-8) is reflected in the y-axis.
=> The y remains the same, the x flips over the y axis to be negative
      (-3,-8)==>>(3,-8)
 
The point (2,4) is reflected in the line x = -3.
=> The x remains the same, the y flips over the x= -3 line.
      Instead of reflecting over the x axis (or the x = 0) line
      and just being +4 or 4 above the x axis to -4 or 4 below the x axis
      you have +4 being 7 above the x= -3 line so you need
      7 below the x= -3 line or -10  SO
       (2,4)==>>(2,-10)
 
The point (a, b) is reflected in the line y = x
      Consider that the line x=y is a 45 degree diagonal.
      Imagine a point on the x axis at +3  i.e. (3,0)
      Imagine a line perpendicular to x=y from the point (3,0)
            (sorry there is no way to draw on here - try drawing it)
     The line would hit the y axis at (0,3)
     So you can see the x becomes y and y becomes x.
      (a,b)==>>(b,a)
 
For
ΔXYZ is defined by its vertices X(1,3), Y(-3,5), and Z(0, -5).
        ΔXYZ is reflected in the y-axis.
So for each of of the 3 points X, Y, and Z reflect them about
        the y axis the same way in the second example above
        and you will have the 3 new points X’,  Y', and Z’
 
The translation T: (x, y) → (x -2, y + 4) maps the point (2, -3) to
The translation T: (x, y) → (x + 3, y - 2) maps the point (-4, -3) to
      What you need to do here is just plug the values for X and Y into the translation.
      e.g. for T: (x, y) → (x -2, y + 4)  plug (2,-3) of x=2 y=-3 into (x -2, y + 4) and get the new values.

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