SOLUTION: Plot the points a(2,2) b(5,5). These two points are the vertices of the figure which is symmetrical about each of the lines given below . Complete the figure on the graph write dow

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y=2,

plot the two points, connect them, and draw the line whose
equation is y=2, a horizontal line thru 2 on the y-axis:



Notice that (2,2) is on the line, points on the
line of reflection reflect into themselves. So
the reflection of (2,2) is itself (2,2).

Notice that (5,5) is 3 units ABOVE the line of
reflection.  So it reflects into a point which
is 3 units BELOW the line.  That point will be
the point (5,-1). See below:



So we see that the reflection of (2,2) IS (2,2)
And the reflection of (5,5) is (5,-1), and the
figure is a triangle.

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x=7

plot the two points, connect them, and draw the line whose
equation is x=7, a vertical line thru 7 on the x-axis.



The point (2,2) is 5 units LEFT of the green line.
So its reflection in that line will be a point 5
units RIGHT of that line.  That will be the point
(12,2). The point (5,5) is 2 units LEFT of the 
green line. So its reflection in that line will 
be a point 5 units RIGHT of that line. That will 
be the point (9,5).

     

So (2,2)'s reflection is (12,2) and (5,5)'s reflection is (9,5).
And the figure is an 'isosceles trapezoid' if you live in the US.
But if you lkive in the UK it is an 'isosceles trapezium'.

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 y=0

plot the two points, connect them, and draw the line.
This time the line is the x-axis for y=0 is the equation
of the horizontal line which is the x-axis.



The point (2,2) is two units ABOVE the x-axis, so its relection
will be to a point which is two units BELOW the x-axis, which is 
the point (2,-2). The point (5,5) is two units ABOVE the x-axis,
so its relection will be to a point which is two units BELOW 
the x-axis, which is the point (5,-5). 



and we see that the figure is another isosceles trapezoid 
(or trapezium, if you live in the UK).

Edwin