QuestionConstruct a figure where $\overline{XY}$ is perpendicular to $\overline{YZ}$ . What are the first and second steps?

Studdy Solution

STEP 1

Assumptions1. We are given that $\overline{XY}$ is perpendicular to $\overline{YZ}$ . . We have to construct the figure accurately.

STEP 2

From the given first step options, we need to start by plotting the points $X, Y$ , and $Z$ . This is because we need these points to draw the lines $\overline{XY}$ and $\overline{YZ}$ .
So, the correct first step is\begin{itemize} \item[D.] Plot the points $X, Y$ , and $Z$ . \end{itemize}

STEP 3

After plotting the points, we need to draw the line $\overline{XY}$ . This is because $\overline{XY}$ is one of the given lines in the problem.
So, the correct second step is\begin{itemize} \item[B.] Draw $\overline{XY}$ . \end{itemize}

STEP 4

Now that we have the line $\overline{XY}$ , we need to draw the line $\overline{YZ}$ such that it is perpendicular to $\overline{XY}$ .To do this, we can use a compass to draw an arc from point $Y$ that intersects $\overline{XY}$ . Then, keeping the compass at the same width, we draw another arc from the point where the first arc intersected $\overline{XY}$ . The point where these two arcs intersect will be point $Z$ , and $\overline{YZ}$ will be perpendicular to $\overline{XY}$ .
So, the correct third step is\begin{itemize} \item[A.] Set the compass to the length of $\overline{XY}$ . Place the compass point on the point $X$ and draw an arc that intersects $\overline{XY}$ on the side of $X$ opposite $Y$ . Label that point $A$ . \end{itemize}

STEP 5

Finally, we connect points $Y$ and $Z$ to form the line $\overline{YZ}$ .
So, the correct fourth step is\begin{itemize} \item[C.] Connect the points $X, Y$ , and $Z$ with lines $\overrightarrow{X}, \overrightarrow{Y}, \overrightarrow{Z}$ , and $\overrightarrow{XZ}$ . \end{itemize}

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