Question

1. draw the image of quadrilateral abcd when translated by the directed line segment v. label the image of a as a, the image of b as b, the image of c as c, and the image of d as d. (from unit 1, lesson 12.)

Explanation:

Step1: Determine translation vector

Observe the directed - line segment \(v\) to find its horizontal and vertical displacements.

Step2: Translate point A

Count the horizontal and vertical units from point \(A\) according to the displacements of \(v\) to find \(A'\).

Step3: Translate point B

Count the horizontal and vertical units from point \(B\) according to the displacements of \(v\) to find \(B'\).

Step4: Translate point C

Count the horizontal and vertical units from point \(C\) according to the displacements of \(v\) to find \(C'\).

Step5: Translate point D

Count the horizontal and vertical units from point \(D\) according to the displacements of \(v\) to find \(D'\).

Step6: Draw the new quadrilateral

Connect \(A'\), \(B'\), \(C'\), and \(D'\) to form the translated quadrilateral \(A'B'C'D'\).

This is a geometric construction task and cannot be fully completed in text - the actual drawing needs to be done on the given grid paper following the above steps. The key is to accurately use the translation vector given by the directed - line segment \(v\) to move each vertex of the quadrilateral.

Answer:

Step1: Determine translation vector

Observe the directed - line segment \(v\) to find its horizontal and vertical displacements.

Step2: Translate point A

Count the horizontal and vertical units from point \(A\) according to the displacements of \(v\) to find \(A'\).

Step3: Translate point B

Count the horizontal and vertical units from point \(B\) according to the displacements of \(v\) to find \(B'\).

Step4: Translate point C

Count the horizontal and vertical units from point \(C\) according to the displacements of \(v\) to find \(C'\).

Step5: Translate point D

Count the horizontal and vertical units from point \(D\) according to the displacements of \(v\) to find \(D'\).

Step6: Draw the new quadrilateral

Connect \(A'\), \(B'\), \(C'\), and \(D'\) to form the translated quadrilateral \(A'B'C'D'\).

This is a geometric construction task and cannot be fully completed in text - the actual drawing needs to be done on the given grid paper following the above steps. The key is to accurately use the translation vector given by the directed - line segment \(v\) to move each vertex of the quadrilateral.