Chapter 13, Problem 1NT

NOW TRY THIS

In Figure 3 use a compass and straightedge to construct the following:

a. The image of A under a translation that takes M to N.

b. The image of A under a translation that takes N to M.

To determine

a.

To construct:

The image of A under a translation that takes M to N by using the given figure.

Answer to Problem 1NT

Solution:

Explanation of Solution

Given:

The figure is given by,

A translation by a slide arrow $\overrightarrow{MN}$ is a transformation of the plane to itself such that every point A in the plane has an image $A^{\prime }$ so that $\overline{A{A}^{\prime }}=\overline{MN}$, $\overline{A{A}^{\prime }}\parallel \overline{MN}$ and the direction from P to $P^{\prime }$ is the same as from M to N.

Draw the image of A under a translation that takes M to N.

From Figure 1, it is observed the image of A is $A^{\prime }$ provided that $\overline{A{A}^{\prime }}=\overline{MN}$ and $\overline{A{A}^{\prime }}\parallel \overline{MN}$.

To determine

b.

To construct:

The image of A under a translation that takes N to M by using the given figure.

Answer to Problem 1NT

Solution:

Explanation of Solution

Given:

The figure is given by,

A translation by a slide arrow $\overrightarrow{NM}$ is a transformation of the plane to itself such that every point A in the plane has an image $A^{\prime }$ so that $\overline{A{A}^{\prime }}=\overline{NM}$, $\overline{A{A}^{\prime }}\parallel \overline{NM}$ and the direction from P to $P^{\prime }$ is the same as from N to M.

Draw the image of A under a translation that takes N to M.

From Figure 12 it is observed the image of A is $A^{\prime }$ provided that $\overline{A{A}^{\prime }}=\overline{NM}$ and $\overline{A{A}^{\prime }}\parallel \overline{NM}$.