Question

Triangle $ABC$ goes through which of the following transformations to obtain the image $DEF?$ Also, choose the correct relation between the corresponding angles of the image and the preimage.

• A. Translation of $1$ unit in right, $\angle D=\angle A,\angle E=\angle B,\text{and}\angle F=\angle C$
• B. Translation of $1$ unit in right, $\angle A=\angle F,\angle B=\angle D,\text{and}\angle C=\angle E$
• C. Clockwise rotation of ${90}^{\circ },\angle B=\angle E,\angle A=\angle F,\text{and}\angle C=\angle D$
• D. Counterclockwise rotation of ${90}^{\circ },\angle A=\angle E,\angle B=\angle D,\text{and}\angle C=\angle F$

Answer 1

The correct option is A Translation of $1$ unit in right, $\angle D=\angle A,\angle E=\angle B,\text{and}\angle F=\angle C$

In the given figure, rotation by ${90}^{\circ }$ will change the orientation of $△ABC$ , but the orientations of the image and the preimage are the same, which means rotation is not the transformation involved here, and thus option $A$ and option $D$ are incorrect.

Now, let’s analyze the translation which is the only transformation left in options $B$ and $C.$


The figure above shows the translation of $ABC\text{to}DEF$ by $1$ unit.

Which means all the coordinates of $△ABC$ are translated $1$ unit to the right to form the image $△DEF$.

From the translation of coordinates, we can conclude that:
$\angle A=\angle D,\angle B=\angle E\text{and}\angle C=\angle F$

Hence, $DEF$ is obtained by translation of $ABC$ by $1$ unit in the right direction and the correct relation of corresponding angles are $\angle A=\angle D,\angle B=\angle E\text{and}\angle C=\angle F.$

➡Option B is correct.