Work two examples and plot on a graph

Question

ScanSolve AI Tutor · Accepted Answer

Okay, let's work through two examples of reflection across the line y = x and plot them.

Example 1:

Consider the point P(3, 1).
To reflect this point across the line y = x, we swap the x and y coordinates.
The reflected point P' will have coordinates (1, 3).
Plot the points.
On a graph, plot P at (3, 1) and P' at (1, 3). Draw the line y = x (a diagonal line passing through the origin with a slope of 1). You will see that P' is the mirror image of P across this line.

Example 2:
Consider the point Q(-2, 4).
To reflect this point across the line y = x, we swap the x and y coordinates.
The reflected point Q' will have coordinates (4, -2).
Plot the points.
On a graph, plot Q at (-2, 4) and Q' at (4, -2). Draw the line y = x. You will see that Q' is the mirror image of Q across this line.

Here's how you would visualize this on a graph:

Imagine a coordinate plane.
Draw the line y = x. This line goes through (0,0), (1,1), (2,2), etc.
For Example 1:
Plot point P at (3, 1) (3 units right, 1 unit up).
Plot point P' at (1, 3) (1 unit right, 3 units up).
Connect P and P' with a dashed line. This line segment should be perpendicular to y = x, and the intersection point should be the midpoint of PP'.

For Example 2:
Plot point Q at (-2, 4) (2 units left, 4 units up).
Plot point Q' at (4, -2) (4 units right, 2 units down).
Connect Q and Q' with a dashed line. This line segment should also be perpendicular to y = x, and the intersection point should be the midpoint of QQ'.

Step-by-step solution