Use the image to answer the question.

Question

Two rays diverge rightward from a vertex point labeled upper Q. One ray extends horizontally through a point labeled upper R, while the other extends diagonally through a point labeled upper P. Points upper R and upper P are connected by an arc.

On her paper, Katarzyna wants to construct the angle bisector of angle ∠PQR
. She has drawn an arc from the vertex point Q
that intersects both sides of the angle and has labeled the intersection of the arc with the sides of the angle with P
and R
. Using a compass and straightedge, what next step must she take to construct the angle bisector?

Option #1: Move the compass further apart and place the pointed end at point Q
and draw another arc that intersects the sides of the angle.

Option #2: Place the pointed end of the compass on point P
and draw another arc inside the first arc and between two sides of the angle.

Option #3: Place the pointed end of the compass on point P
and draw another arc outside the first arc and between two sides of the angle.

Option #4: Draw a line extending from the vertex point Q
through the middle of the angle.

(1 point)
Katarzyna’s next step is Option #
.

Answer 1

Katarzyna has already drawn an arc from the vertex point Q that intersects both sides of the angle at points P and R. The next step in constructing the angle bisector would involve using the positions of these intersection points (P and R) to find the bisector.

The correct option would be to place the pointed end of the compass on point P and draw another arc inside the first arc and between the two sides of the angle. This step will help her find the points where these two arcs intersect, which will be used to locate the angle bisector.

Therefore, Katarzyna’s next step is Option #2.