# Question Video: Finding the Magnitude and Direction of a Given Translation Mathematics • 11th Grade

Fill in the blank: In the figure, the triangles 𝑋𝐿𝑀, 𝐿𝑌𝑁, 𝑁𝑀𝐿, and 𝑀𝑁𝑍 are congruent. △𝐿𝑌𝑁 is the image of △𝑀𝑁𝑍 by a translation of magnitude ＿ in the direction of ＿.

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### Video Transcript

Fill in the blank. In the figure, the triangles 𝑋𝐿𝑀, 𝐿𝑌𝑁, 𝑁𝑀𝐿, and 𝑀𝑁𝑍 are congruent. The triangle 𝐿𝑌𝑁 is the image of the triangle 𝑀𝑁𝑍 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 𝑀𝑁𝑍 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, 𝑀, and determine its image under the translation. The two triangles 𝑀𝑁𝑍 and 𝐿𝑌𝑁 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 𝐿 is the image of the top vertex of the original triangle 𝑀. The magnitude of the translation is therefore given by the distance between 𝑀 and 𝐿, 𝑀𝐿. And the direction is given by the direction of the ray starting at the vertex 𝑀 and passing through 𝐿, 𝑀𝐿. Therefore, the answer is (A).