Question

sketch the figure described. explain how to construct it. then do the construction.

\\(\overleftrightarrow{xy} \perp \overleftrightarrow{yz}\\)

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

Explanation:

Identify the geometric description and correct sketch

$$ \overleftrightarrow{XY} \perp \overleftrightarrow{YZ} $$

The intersection point must be \(Y\).
Option A shows line \(XY\) and line \(YZ\) intersecting perpendicularly at point \(Y\).
Option B shows the intersection at an unlabeled point, with \(Y\) on the horizontal line and \(Z\) on the vertical line, which is incorrect.

Determine the first step of construction

To construct perpendicular lines, the first step is to establish the base line.
The base line is \(\overleftrightarrow{XY}\).
Therefore, the first step is to draw \(\overleftrightarrow{XY}\).

Answer:

Question 1

• (A) A sketch showing line XY and line YZ intersecting perpendicularly at point Y. (Correct answer)
• (B) A sketch showing the intersection at an unlabeled point, with Y on the horizontal line and Z on the vertical line.

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.