### Penciling

In laying out the border lines and center lines follow the directions given for Plate IV. Draw the dot and dash lines in the same manner, as there are to be six problems on this plate.

## Problem 7. How To Draw A Perperidicular To A Line From A Point Without The Line

Draw the straight line A C about 3 1/4 inches long, and assume the point P about 1 1/2 inches above the line. With P as a center and any convenient radius - about 2 inches - describe an arc cutting A C at E and F. The radius of this arc must always be such that it will cut A C in two points; the nearer the points E and F are to A and C, the greater will be the accuracy of the work.

Now with E and F as centers and any convenient radius - about 2 1/4 inches - draw the arcs intersecting below A C at T. A line through the points P and T will be perpendicular to AC. In case there is not room below A C to draw the arcs, they may be drawn intersecting above the line as shown at N. Whenever convenient draw the arcs below A C for greater accuracy.

### Proof

Since P and T are both equally distant from E and F, the line P T is perpendicular to A C.