Question

sketch the figure described. choose the correct answer below.

explain how to construct the figure accurately. what is the first step?

a. draw \\(\overleftrightarrow{xy}\\) perpendicular to \\(\overleftrightarrow{yz}\\).
b. draw \\(\overleftrightarrow{xz}\\).
c. draw \\(\overleftrightarrow{xy}\\).
d. plot the points x, y, and z

what is the second step of the construction?

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.
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}\\).

Explanation:

Identify the correct sketch

The top of the image shows a prompt: "Sketch the figure described." (The description is cut off but can be inferred from the options: line \(XY\) perpendicular to line \(YZ\) at point \(Y\)).

• Option A shows line \(\overleftrightarrow{XY}\) horizontal with point \(X\) and point \(Y\) on it, and a perpendicular line \(\overleftrightarrow{YZ}\) passing through \(Y\) and \(Z\). The right-angle symbol is at \(Y\).
• Option B shows a horizontal line with points \(X\) and \(Y\), but the perpendicular line passes through a point that is not \(Y\).
• Therefore, Option A is the correct sketch.

Determine the first step of the construction

To construct a line perpendicular to a given line at a point on the line:

• First, you must establish the base line.
• The correct first step is to draw the line \(\overleftrightarrow{XY}\).
• This corresponds to Option C.

Determine the second step of the construction

To construct a perpendicular at point \(Y\) on line \(\overleftrightarrow{XY}\):

• You need to find a point \(A\) on the line \(\overleftrightarrow{XY}\) such that \(Y\) is the midpoint of segment \(XA\).
• This is done by setting the compass to the length of \(\overline{XY}\), placing the compass point on \(Y\), and drawing an arc that intersects \(\overleftrightarrow{XY}\) on the side of \(Y\) opposite \(X\). Label that point \(A\).
• This corresponds to Option A.

Answer:

Question 1

• (A) Sketch A (Correct answer)
• (B) Sketch B

Question 2

• (A) Draw \(\overleftrightarrow{XY}\) perpendicular to \(\overleftrightarrow{YZ}\).
• (B) Draw \(\overleftrightarrow{XZ}\).
• (C) Draw \(\overleftrightarrow{XY}\). (Correct answer)
• (D) Plot the points X, Y, and Z

Question 3

• (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 \(\overleftrightarrow{XZ}\).