Question

1. draw the image of \\( \triangle a b c \\) after a translation along \\( \vec{v} \\).
2. in your own words, explain what a translation of a figure is.

describe how the direction of the above vector \\( \vec{v} \\) is moving \\( \triangle a b c \\).

Explanation:

Step1: Determine the horizontal and vertical components of the vector

Count the number of units moved horizontally and vertically. From the grid, the vector \(\vec{v}\) moves \(4\) units to the right (positive \(x -\)direction) and \(3\) units down (negative \(y -\)direction).

Step2: Translate each vertex of \(\triangle ABC\)

Let the coordinates of \(A=(x_1,y_1)\), \(B=(x_2,y_2)\), \(C=(x_3,y_3)\). After translation, the new coordinates will be \(A'=(x_1 + 4,y_1-3)\), \(B'=(x_2 + 4,y_2-3)\), \(C'=(x_3 + 4,y_3-3)\). For example, if \(A=(0,0)\) (assuming a starting - point for simplicity, based on the grid), then \(A'=(4,-3)\); if \(B=(0,3)\), then \(B'=(4,0)\); if \(C=(5,0)\), then \(C'=(9,-3)\). Then connect the points \(A'\), \(B'\), and \(C'\) to form the translated triangle.

Step3: Describe the translation in words

A translation is a type of transformation. The vector \(\vec{v}\) has a direction. We can describe the direction of the vector \(\vec{v}\) by looking at its horizontal and vertical displacements. The vector \(\vec{v}\) moves the triangle \(4\) units to the right (in the positive \(x -\)axis direction) and \(3\) units down (in the negative \(y -\)axis direction).

Answer:

1. (After performing the coordinate - based translation as described in Step 2, draw the triangle with vertices \(A'\), \(B'\), \(C'\)).
2. The vector \(\vec{v}\) moves \(\triangle ABC\) \(4\) units to the right and \(3\) units down.