Question 424292
A(1, 2), B(4,2) and C(6,4). 
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Draw the original triangle:

{{{drawing(400,400,-8,8,-8,8,
locate(1,2,"(1,2)"),locate(4,2,"(4,2)"),locate(6,4,"(6,4)"), 
graph(400,400,-8,8,-8,8), triangle(1,2,4,2,6,4) )}}} 

Reflect it in the x-axis, we get the green triangle:

{{{drawing(400,400,-8,8,-8,8,
locate(1,2,"(1,2)"),locate(4,2,"(4,2)"),locate(6,4,"(6,4)"), 
graph(400,400,-8,8,-8,8), triangle(1,2,4,2,6,4),

green(locate(1,-1.3,"(1,-2)"),locate(4,-1.3,"(4,-2)"),locate(6,-3.3,"(6,-4)"), 
triangle(1,-2,4,-2,6,-4))



 )}}}

So reflecting in the x-axis keeps the x coordinate 
and changes the sign of the y-coordinate.

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Reflect it in the origin, this green triangle:

{{{drawing(400,400,-8,8,-8,8,
locate(1,2,"(1,2)"),locate(4,2,"(4,2)"),locate(6,4,"(6,4)"), 
graph(400,400,-8,8,-8,8), triangle(1,2,4,2,6,4),

green(locate(-3,-1.3,"(-1,-2)"),locate(-6.5,-1.3,"(-4,-2)"),locate(-8,-3.3,"(-6,-4)"), 
triangle(-1,-2,-4,-2,-6,-4))



 )}}}

So reflecting in the origin changes the sign of BOTH coordinates.


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A dilation of 2 from the origin, this green triangle

{{{drawing(800,800,-16,16,-16,16,
locate(1,2,"(1,2)"),locate(4,2,"(4,2)"),locate(6,4,"(6,4)"), 
graph(800,800,-16,16,-16,16), triangle(1,2,4,2,6,4),

green(locate(2,4,"(2,4)"),locate(8,4,"(8,4)"),locate(12,8,"(12,8)"), 
triangle(2,4,8,4,12,8))



 )}}}


Both coordinates are multiplied by 2.

Edwin</pre>