Question

8.
on point y on line x, construct a line
perpendicular to x through y.

Explanation:

Step1: Place the compass at point Y

Open the compass to a convenient radius.

Step2: Draw arcs intersecting line x

Draw two arcs on line x on either side of point Y. Let the intersection points be A and B.

Step3: Adjust the compass radius

Make the radius larger than half of the distance between A and B.

Step4: Draw arcs from A and B

From points A and B, draw arcs above (or below) line x such that these two arcs intersect. Let the intersection point be C.

Step5: Draw the perpendicular line

Connect point Y and point C. The line YC is perpendicular to line x.

Answer:

The constructed line YC is perpendicular to line x through point Y.