QuestionConstruct the perpendicular bisector of segment $\overline{AB}$ . What is the first step? A, B, C, or D? What is the second step? B or C?

Studdy Solution

STEP 1

Assumptions1. The segment $\overline{\mathrm{AB}}$ has already been constructed. . We have a compass and a straightedge for the construction.

STEP 2

The first step in constructing the perpendicular bisector of $\overline{\mathrm{AB}}$ is to put the compass point on point $A$ and draw a long arc. Be sure the opening is greater than $\frac{1}{2} A B$ . This is represented by option B in the given choices.
$\text{Put the compass point on point } A \text{ and draw a long arc. Be sure the opening is greater than } \frac{1}{2} AB.$

STEP 3

The second step is to keep the same compass setting, put the compass point on point $B$ and draw another long arc. The points where the two arcs intersect each other are labeled as $X$ and $Y$ . This is represented by option B in the given choices.
$\text{With the same compass setting, put the compass point on point } B \text{ and draw another long arc. Label the points where the two arcs intersect each other as } X \text{ and } Y.$

STEP 4

The last step is to draw a line through points $X$ and $Y$ . This line is the perpendicular bisector of $\overline{\mathrm{AB}}$ .
$\text{Draw a line through points } X \text{ and } Y. \text{ This line is the perpendicular bisector of } \overline{\mathrm{AB}}.$

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