Question

1. in a new translation, the image of v is z. find at least 3 other points that are taken to a labeled point by the new translation.

Explanation:

Step1: Recall translation concept

Translation is a rigid - motion that moves every point of a figure or a space by the same distance in a given direction. If the image of point V is Z, we need to find the vector from V to Z. Then we can apply this vector to other points.

Step2: Assume we know the coordinates (or relative positions) of points

Let's assume we can determine the horizontal and vertical displacements from V to Z. If the horizontal displacement is \(x\) units and the vertical displacement is \(y\) units, for any point \(P(x_1,y_1)\), its new - translated point \(P'(x_2,y_2)\) has coordinates \(x_2=x_1 + x\) and \(y_2=y_1 + y\).

Step3: Choose points and apply translation

Let's say we have points A, B, C. We find their new positions by adding the horizontal and vertical displacements (determined from the V - to - Z translation) to the coordinates of A, B, C respectively. For example, if point A has coordinates \((a_1,a_2)\), its new coordinates \(A'(a_1 + x,a_2 + y)\).

Let's assume some points for illustration. Suppose the translation vector from V to Z is \((3,2)\) (3 units to the right and 2 units up). If we have point A with coordinates \((1,1)\), its new coordinates \(A'(1 + 3,1+ 2)=(4,3)\); if point B has coordinates \((2,3)\), its new coordinates \(B'(2 + 3,3 + 2)=(5,5)\); if point C has coordinates \((0,0)\), its new coordinates \(C'(0+3,0 + 2)=(3,2)\).

Answer:

For example, if the translation that maps V to Z is a shift of 3 units to the right and 2 units up, and we choose points A, B, C with original coordinates \((1,1)\), \((2,3)\), \((0,0)\) respectively, their new coordinates after translation are \((4,3)\), \((5,5)\), \((3,2)\)