Chapter 10.8, Problem 1WE

a)

To determine

To construct: a perpendicular to $\overline{AB}$ .

Explanation of Solution

Given Information:

Draw any $\overline{AB}$ and a segment with length $h$ . Use the following steps to construct the locus of points $P$ such that for every $\Delta APB$ the altitude from $P$ to $\overleftrightarrow{AB}$ would equal $h$ .

Calculation:

Draw a line $\overline{AB}$ .

Construct a perpendicular on $\overline{AB}$ by choosing any point $X$ on $\overline{AB}$ and making arcs on both sides of the point, $O$ and $P$ .

Now put the compass needle on $O$ and make an arcs as $Q$ , now put the compass needle at $P$ and intersect the arc at $Q$ .

Join the points $Q$ and $X$ .

  

  $\overline{QX}$ is perpendicular on $\overline{AB}$ .

b)

To determine

To construct: two lines parallel to $\overline{AB}$ , $h$ units from $\overline{AB}$ .

Explanation of Solution

Given Information:

Draw any $\overline{AB}$ and a segment with length $h$ . Use the following steps to construct the locus of points $P$ such that for every $\Delta APB$ the altitude from $P$ to $\overleftrightarrow{AB}$ would equal $h$ .

Calculation:

Draw a line $\overline{AB}$ .

Construct a perpendicular on $\overline{AB}$ at $X$ .

Make arcs from $X$ for a length $h$ at $P$ and $S$ .

Construct a perpendicular on $\overline{PX}$ at $P$ . $l$ is parallel to $\overline{AB}$ and $h$ units from $\overline{AB}$ .

Similarly construct a perpendicular on $\overline{XS}$ at $S$ . $m$ is parallel to $\overline{AB}$ and $h$ units from $\overline{AB}$ .