What will the coordinates (-5,3) be once flipped over the y-axis?

Question

I'm confused as to how to change coordinates when they flip over the x and y axis.

Answer 1

The easiest way to answer this question is to visualize a graph with the indicated point (-5,3) on it. If you wanted to flip this point over the y-axis, you could just imagine folding the graph in half along the y-axis, and wherever your original point ends up is where your new point will be. 

 

In this case, you would have a point that is at the same y-value, but the x-value will have become 5 (the negative of what it was). So your new coordinate will be (5,3)

 

Simply put, if you want to flip a point over the y-axis, just multiply the x-component by -1, and if you want to flip a point over the x-axis, just multiply the y-component by -1.

Answer 2

"Flip" (x, y) over x-axis → (x, -y)

 

"Flip" (x, y) over y-axis → (-x, y)

 

So, (-5, 3) flipped over the y-axis is: (-(-5), (3)) → (5, 3)

Answer 3

If you draw it on a grid it will help you see why this is true, but in general when you reflect (or flip) over an axis, the value that goes along with that axis stays the same and the other value becomes the negative of itself.

 

Since (-5,3) is 5 units left of the y-axis, flipping over the y axis would move it straight across the axis until you ended up 5 units to the right of the y-axis, but it would keep the y value exactly the same.  The new point would be (5,3).

 

If we flipped it over the x-axis, the x value would stay the same and the point would move straight down across the axis until it got to -3.  So the point would be (-5,-3).

 

Drawing quick sketches for these types of problems should help you get used to the idea.