Question

The position of lawn $ABC$ is transformed and a new image is formed. What type of transformation is it?

• A. Reflection
• B. Rotation
• C. Translation
• D. Dilation

Answer 1

The correct option is C Translation

Coordinates of the triangle $=A(2,2),B(2,4),C(5,5)$
Coordinates of the triangle after transformation $=A^{\prime }(4,2),B^{\prime }(4,4),C^{\prime }(7,5)$
From the coordinates, we can observe that the y-coordinate of each vertex of the preimage and the image are the same. There is a change in the $x$-coordinate only.
By observing the image and the preimage in the coordinate plane, it is clear that the figure has moved toward the right to get the image.
The transformation in which the figure slides is called translation.
In translation, all the points of the object are moved in a straight line in the same direction.
Let’s assume that the $x$-coordinate of each point in the preimage is moved by $x$ units to the right.
Hence, $A^{\prime }(2+x,2),B^{\prime }(2+x,4),C^{\prime }(5+x,5)=A^{\prime }(4,2),B^{\prime }(4,4),C^{\prime }(7,5).$
Now, comparing the coordinates, we have:
$2+x=4$
$\Rightarrow x=4-2$
$\Rightarrow x=2$

The triangle is translated 2 units toward the right.

Hence, the correct answer is option A.