Question

Reflect the diamond-shaped polygon whose vertices are a (-1,0), b (0,-2), c (1,0) and d (0,2) about (1) the horizontal line y=2 (2) the vertical line x=2

Answer 1

We have been given a diamond-shaped polygon whose vertices are a (-1,0), b (0,-2), c (1,0) and d (0,2).

Now we need to reflect these points about line horizontal line y=2

Easiest way to do that is, graph the given points then count how many units they are away from the line y=2. Then shift the point by twice of that unit upward.

For example point (-1,0) is 2 unit away from the line y=2.

twice of 2 is 4. So we shift the point (-1,0) upward by 4 units. which gives (-1,0+4)=(-1,4).

Same way you can reflect other points.

So the points after reflection about line y=2 will be:

a(-1,4), b(0,6), c(1,4), d(0,2)

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Same process is for reflection about line x=2

From graph we see that points are on the left side of line x=2 so count how many units they are away from the line x=2 then move each point twice of that distance on right side.

For example point (-1,0) is 1 3 units away from line x=2.

Twice of 3 is 6 so we will move the point 6 units to the right which is (-1+6,0)=(5,0)

Repeat same process for other points

So the points after reflection about line x=2 will be:

a(5,0), b(4,-2), c(3,0), d(4,2)