What is the image of (-3,6) when reflected in the x-axis?

Answer 1

First, mark the point (-3, 6) on the graph.

When the question is: Reflection in the x-axis- imagine a mirror on the x-axis, the point on the other side would be equidistant from the x-axis, that is, (-3 ,-6 ),' -6 ' as Y would be negative in the 3rd quadrant, where the image is reflected.

The above is general understanding for this scenario.

There are 2 rules we get from the above explanation:-

1) (x,y) reflects across x-axis as (x ,-y ).

2) (x,y) reflects across y-axis as (-x, y).

Hope this helps!

Answer 2

There are two ways we can solve this. I'd learn the first way and then resort to the second once you understand the first.

First Way - Drawing/Distance

Let's draw this out -- draw the point (-3,6) on a chart. The X-axis -- the line y=0 -- is the horizontal line on your axis itself. What we are doing is "mirroring" our point across this line. The distance this point has from the x-axis has to be the same after we mirror it.

So, what's the distance it has from the x-axis? Well, if we're reflecting it across the x-axis, we know the x value itself, by definition won't change. This is because we are only concerned with moving the point vertically (hence, reflecting it across the horizontal access). We can count the distance it has from the x-axis itself-- in this case, it is 6! So, to reflect it across the x axis, we keep the same x coordinate (-3), and just move it down 6. Thus, the image reflected it (-3,-6).

Second Way - X-Axis/Y-Axis Reflection Definition

The second way is a product of the first. Whenever something is reflected JUST across the x-axis and the y-axis, we negate one of the numbers in the point itself. If we reflect across the x-axis, we negate the y-term (as we did above). If we reflect across the y-axis, we negate the x-term. Thus, in this case, we would just negate the y-term, leaving us with (-3,-6). I encourage you to think about why this is always true!