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.

Explanation:

Interpret the geometric notation

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

The notation represents line \(XY\) perpendicular to line \(YZ\). The common point of intersection is \(Y\).

Analyze the given options

• Option A shows a horizontal line containing points \(X\) and \(Y\), and a vertical line containing point \(Z\) intersecting at point \(Y\). Thus, the horizontal line is \overleftrightarrow{XY} and the vertical line is \overleftrightarrow{YZ}, which are perpendicular at \(Y\).
• Option B shows a horizontal line containing points \(X\) and \(Y\), and a vertical line containing point \(Z\) intersecting at a point other than \(Y\).

Select the correct option

Option A correctly represents \overleftrightarrow{XY} intersecting \overleftrightarrow{YZ} perpendicularly at point \(Y\).

Answer:

• (A) horizontal line through X and Y, perpendicular vertical line through Y and Z (Correct answer)
• (B) horizontal line through X and Y, perpendicular vertical line through Z intersecting elsewhere