Question

a. set the compass to the length of \\(xy\\). place the compass point on the point \\(y\\) and draw an arc that intersects \\(\overleftrightarrow{xy}\\) on the side of \\(y\\) opposite \\(x\\). label that point \\(a\\).
b. set the compass to the length of \\(xy\\). place the compass point on the point \\(x\\) and draw an arc that intersects \\(\overleftrightarrow{xy}\\) on the side of \\(x\\) opposite \\(y\\). label that point \\(a\\).
c. set the compass to the length of \\(\overline{xz}\\). place the compass point on the point \\(z\\) and draw an arc that intersects \\(\overleftrightarrow{xz}\\) on the side of \\(z\\) opposite \\(x\\). label that point \\(a\\).
d. connect the points \\(x\\), \\(y\\), and \\(z\\) with lines \\(\overleftrightarrow{xy}\\), \\(\overleftrightarrow{yz}\\), and \\(\overleftrightarrow{xz}\\).

what is the final step of the construction?

a. construct the perpendicular bisector of \\(\overline{ya}\\). label any point on the bisector (that is not \\(x\\)) as \\(z\\).
b. construct the perpendicular bisector of \\(\overline{xy}\\). label any point on the bisector (that is not \\(a\\)) as \\(z\\).
c. construct the perpendicular bisector of \\(\overline{za}\\). label any point on the bisector (that is not \\(y\\)) as \\(x\\).
d. construct the perpendicular bisector of \\(\overline{xa}\\). label any point on the bisector (that is not \\(y\\)) as \\(z\\).

what does the final construction look like? choose the correct answer below.

Explanation:

Analyze the first construction step

The first question has option A selected with a green checkmark: "Set the compass to the length of \(\overline{XY}\). Place the compass point on the point \(Y\) and draw an arc that intersects \(\overleftrightarrow{XY}\) on the side of \(Y\) opposite \(X\). Label that point \(A\)." This establishes point \(A\) such that \(Y\) is the midpoint of segment \(\overline{XA}\), meaning \(XY = YA\).

Analyze the final step of the construction

To construct a perpendicular line through point \(Y\) on the line \(\overleftrightarrow{XY}\), we use the equidistant points \(X\) and \(A\) on either side of \(Y\). The final step is to construct the perpendicular bisector of the segment \(\overline{XA}\). This bisector will pass through \(Y\) and any point on this bisector (not \(Y\)) can be labeled as \(Z\). This matches option D: "Construct the perpendicular bisector of \(\overline{XA}\). Label any point on the bisector (that is not \(Y\)) as \(Z\)."

Identify the correct final construction diagram

The construction involves:

1. A line containing points \(X\), \(Y\), and \(A\) in that order, where \(XY = YA\). An arc centered at \(Y\) with radius \(XY\) is drawn to locate \(A\).
2. The perpendicular bisector of \(\overline{XA}\) is constructed, which passes vertically through \(Y\). Point \(Z\) lies on this vertical line.

Diagram A correctly shows the line with points \(X\), \(Y\), and \(A\), the arc centered at \(Y\) passing through \(X\) and \(A\), and the perpendicular bisector of \(\overline{XA}\) passing through \(Y\) with point \(Z\) labeled on it.

Answer:

Question 1

• (A) Set the compass to the length of \(\overline{XY}\). Place the compass point on the point \(Y\) and draw an arc that intersects \(\overleftrightarrow{XY}\) on the side of \(Y\) opposite \(X\). Label that point \(A\). (Correct answer)
• (B) Set the compass to the length of \(\overline{XY}\). Place the compass point on the point \(X\) and draw an arc that intersects \(\overleftrightarrow{XY}\) on the side of \(X\) opposite \(Y\). Label that point \(A\).
• (C) Set the compass to the length of \(\overline{XZ}\). Place the compass point on the point \(Z\) and draw an arc that intersects \(\overleftrightarrow{XZ}\) on the side of \(Z\) opposite \(X\). Label that point \(A\).
• (D) Connect the points \(X\), \(Y\), and \(Z\) with lines \(\overleftrightarrow{XY}\), \(\overleftrightarrow{YZ}\), and \(\overleftrightarrow{XZ}\).

Question 2

• (A) Construct the perpendicular bisector of \(\overline{YA}\). Label any point on the bisector (that is not \(X\)) as \(Z\).
• (B) Construct the perpendicular bisector of \(\overline{XY}\). Label any point on the bisector (that is not \(A\)) as \(Z\).
• (C) Construct the perpendicular bisector of \(\overline{ZA}\). Label any point on the bisector (that is not \(Y\)) as \(X\).
• (D) Construct the perpendicular bisector of \(\overline{XA}\). Label any point on the bisector (that is not \(Y\)) as \(Z\). (Correct answer)

Question 3

• (A) vertical perpendicular line through \(Y\) with points \(X\), \(Y\), \(A\) on the horizontal line (Correct answer)
• (B) vertical perpendicular line through \(A\) with points \(X\), \(A\), \(Y\) on the horizontal line
• (C) vertical perpendicular line through \(A\) with two arcs centered at \(X\) and \(Y\)
• (D) vertical perpendicular line through \(Y\) with two arcs centered at \(X\) and \(A\)