Question

sketch the figure described. choose the correct answer below.

explain how to construct the figure accurately. what is the first step?
a. plot the points x, y, and z
b. draw \\(\overleftrightarrow{xy}\\) perpendicular to \\(\overleftrightarrow{yz}\\).
c. draw \\(\overleftrightarrow{xy}\\).
d. draw \\(\overleftrightarrow{xz}\\).

what is the second step of the construction?
a. connect the points x, y, and z with lines \\(\overleftrightarrow{xy}\\), \\(\overleftrightarrow{yz}\\), and \\(\overleftrightarrow{xz}\\).
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{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.
d. 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.

Explanation:

Identify the correct sketch

The problem asks to sketch the figure described. Looking at the options:

• Option A shows line \(\overleftrightarrow{XY}\) and line \(\overleftrightarrow{YZ}\) perpendicular to each other, with point \(Y\) at the intersection.
• Option B shows the perpendicular line passing through a point between \(X\) and \(Y\), which is incorrect since the perpendicular line is \(\overleftrightarrow{YZ}\), meaning \(Y\) must lie on the intersection.
• Therefore, Option A is the correct sketch.

Determine the first step of construction

To construct the figure accurately:

• We must first establish a base line.
• The first step is to draw the line \(\overleftrightarrow{XY}\).
• Therefore, Option C is the correct first step.

Determine the second step of construction

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

• We need to find a point \(A\) on the opposite side of \(Y\) from \(X\) such that \(Y\) is the midpoint of segment \(XA\).
• This is done by setting the compass to the length of segment \(\overline{XY}\), placing the compass point on \(Y\), and drawing an arc that intersects \(\overleftrightarrow{XY}\) on the side of \(Y\) opposite \(X\), labeling that point \(A\).
• Therefore, Option C is the correct second step.

Answer:

Question 1

• (A) [Sketch showing the perpendicular intersection at point Y] (Correct answer)
• (B) [Sketch showing the perpendicular intersection not at point Y]

Question 2

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

Question 3

• (A) Connect the points X, Y, and Z with lines \(\overleftrightarrow{XY}\), \(\overleftrightarrow{YZ}\), and \(\overleftrightarrow{XZ}\).
• (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 \(\overline{XY}\). 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)
• (D) 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.