Video Transcript
Fill in the blank. In the figure, the triangles
ππΏπ, πΏππ, πππΏ, and πππ are congruent. The triangle πΏππ is the
image of the triangle πππ by a translation of magnitude what in the direction
of what.
The magnitude of a translation
is equivalent to the distance between a point and its image under the
translation. And the direction of a
translation can be described by the ray from a point passing through its
image. The whole triangle πππ can
be translated by translating its vertices. Therefore, we can determine the
magnitude and direction of the translation of the triangle by finding the image
under the translation of just one of its vertices.
So we can pick a vertex, for
example, π, and determine its image under the translation. The two triangles πππ and
πΏππ are highlighted here as the orange and purple triangles,
respectively. Translations do not affect the
scale or orientation of a shape. Therefore, the relative
positions of the vertices in the triangle will remain the same. The top vertex will remain at
the top, and so on.
Therefore, the top vertex of
the image triangle πΏ is the image of the top vertex of the original triangle
π. The magnitude of the
translation is therefore given by the distance between π and πΏ, ππΏ. And the direction is given by
the direction of the ray starting at the vertex π and passing through πΏ,
ππΏ. Therefore, the answer is
(A).
