QuestionConstruct the perpendicular bisector of $\overline{AB}$ .
After drawing an arc through $A$ , what’s the next step?
Final step options: Draw $\overline{BX}$ , $\overline{XY}$ , or locate $M$ .

Studdy Solution

STEP 1

Assumptions1. We have a line segment $\overline{AB}$ . . We have a compass.
3. We have already drawn a long arc through point $A$ with the compass opened to a quarter or half the length of $AB$ .

STEP 2

The second step of the construction is to keep the same compass setting, put the compass point on point $B$ and draw another long arc. This arc should intersect with the previous arc at two points.
$\text{With the same compass setting, put the compass point on point } B \text{ and draw another long arc.}$

STEP 3

Label the points where the two arcs intersect as $X$ and $Y$ .
$\text{Label the points where the two arcs intersect as } X \text{ and } Y.$

STEP 4

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

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