Plot the point that is symmetric to (3,3) with respect to ​(a) the​ x-axis; ​(b) the​ y-axis; ​(c) the origin.

Question

​(a) Plot the point that is symmetric to

(3,3)

with respect to the​ x-axis.

Answer 1

if (x,y) is the point, (x,-y) is symmetric about the x axis, just change the sign of the y coordinate

and (-x,y) is symmetric about the y axis. Just change the sign of the x coordinate

and (-x,-y) is symmetric about the origin. Just change both signs of the coordinates

so for (3,3)

a) (3,-3)

b) (-3,3)

c) (-3,-3)

Answer 2

Symmetric means both sides are the same, like a mirror image. If I stand straight on to a mirror, my reflection isn't at an angle, and it's also the same "distance" in the mirror as I'm standing. My mirror image won't appear closer or farther away.

So, let's look at (3,3). It's 3 to the right of the y-axis (where x = 0) and 3 above the x-axis (where y = 0), right?

a) To reflect the point across the x-axis, it simply moves vertically the same distance to the other side of the x-axis. What's 3 below the x-axis? (3,-3).

b) To reflect across the y-axis, we move horizontally, again equidistant to the other side of the y-axis. What's 3 to the left of the y-axis? (-3,3).

c) Since the origin is at (0,0), where the axes meet, we're doing a combination of the two to reflect across the origin. If I go 3 down from the x-axis aaaaand 3 down from the y-axis, I'm now at (-3-3), right?

Just for fun, let's reflect (3,3) with respect to (1,1). Since we are 2 away both vertically and horizontally, where am I at if I go 2 the other direction from (1,1)? Two down is (1,-1) and two left is (-1,-1), so my reflected point is at (-1,-1).

In all cases, you should be able to draw a straight line from your two points with the reflection point being halfway, aka, the midpoint.

I hope this helps!