Mirror a Coordinate

A coordinate can cross a mirror line without both numbers changing. Surprising? Watch one point slide straight across the grid... and notice which coordinate stays completely still.

A point appears at three, two. Read across first to find three on the horizontal x-axis. Then move up to two on the vertical y-axis. X comes first - never read the vertical coordinate first. Now the y-axis glows as the mirror line. The point is three squares to its right. Its image must land three squares to its left, directly opposite. A dotted horizontal path shows the equal distance on each side. Look carefully... the up-and-down position has not moved. So the y-coordinate stays two. Only the x-coordinate changes sign, from positive three to negative three. Reflection is a flip across the stated axis, not a turn around the origin.

Let's work through an example. On a coordinate grid, point P is at four, negative three. Reflect point P in the y-axis. What are the coordinates of its image, P prime? First, place P. Move four squares right along the x-axis. Then move three squares down, because the y-coordinate is negative three. The point settles in the lower-right part of the grid. The mirror is the vertical y-axis. Count four squares from P to that axis. Now count four squares beyond it, staying on the same horizontal level. P prime appears on the left. Check each coordinate. The horizontal position changes from positive four to negative four. The vertical position remains negative three. So P prime is negative four, negative three. Equal distance, opposite side... solved!

When you reflect one point, read x before y, find the stated mirror axis, then place the image the same perpendicular distance on the opposite side. A y-axis reflection changes x and keeps y. One coordinate moves; the other stays loyal to its line. Spot the axis, count the gap, and you can reflect any single coordinate with confidence, clearly every time!