FOLLOW THE STEPS TO MAKE THE CONSTRUCTION. WILL MARK BRAINLIEST!! THIS IS ONE QUESTION JUST FOLLOW THE STEPS. Step 1:
Using a straightedge, draw a line segment. Draw endpoints and label them P and Q.

Step 2:
Draw a new point that is not on PQ¯¯¯¯¯¯¯¯ and label the point N.

Step 3:
Use a compass to match the distance of PQ¯¯¯¯¯¯¯¯. Do not change the compass setting.

Step 4:
Keep the compass setting from Step 3 and place the needle of your compass on point N and draw an arc (part of a circle).

Step 5:
Draw a point on the arc and label the point M.

Step 6:
Using a straightedge, draw a segment that connects N to M.

Step 7:
Using a ruler, measure PQ¯¯¯¯¯¯¯¯ and MN¯¯¯¯¯¯¯¯¯¯. Write those measures on your construction.

Verify that the distance of each segment has the same measure: PQ=MN.

for the friend request.

when a figure, such as triangle (xyz) is reflected over the line y = x to create x'y'z' the x-coordinates and y-coordinates of the original image (pre-image) will be reversed for the image. (e.g., (x, y) > (y, x)) this means that the pre-image position of the x- and y-coordinates switch places which in turn provides a mirror like image of the original xyz.  

i notice that when i draw a line segment from x to x', that the points are parallel from each other -- they are exactly across from each other and do not intersect with any other points.  

yes, think i would see the same characteristic if you drew the line segment connecting y with the reflecting line and then y' with the reflecting line because of the essence of reflections. because it is a mirror image, each point was effected the same way which leads me to conclude that they same would apply to y and y'.