Question

Draw a line $l$ and a point $X$ on it. Through $X$, draw a line segment perpendicular to $l$.Now draw a perpendicular to $\overline{XY}$ at $Y$. (use ruler and compasses)

Answer 1

Step 1: Draw a line l and mark a point X on it.

Step 2: Take $X$ as centre and with a convenient radius, draw an arc intersecting the line $l$ at points A and B, respectively.

Step 3: Take A and B as centres and a radius more than AX, construct two arcs such that they intersect each other at point Y.

Step 4: Join XY. Here is perpendicular to $l$.

Step 5: Take C and D as centers and radius more than CY, construct two arcs intersecting at point Z. Join ZY. The line $\overline{ZY}$ ia perpedicular to the line $\overline{XY}$.