Question

The figure shows Polygon ABCD and some of its transformed images on a coordinate grid: A coordinate plane is shown. Figure ABCD has endpoints negative 5 comma 5, negative 5 comma 2, negative 3 comma 1 and negative 3 comma 3. Figure 1 has endpoints negative 1 comma 1, negative 1 comma 3, 1 comma 5 and 1 comma 2. Figure 2 has endpoints 3 comma 1, 3 comma 3, 5 comma 5 and 5 comma 2. Figure 3 has endpoints 1 comma 1, 1 comma negative 2, 3 comma negative 1 and 3 comma negative 3. Figure 4 has endpoints negative 3 comma negative 1, negative 3 comma negative 3, negative 5 comma negative 2, and negative 5 comma negative 5. Which of the four polygons was formed by a translation of Polygon ABCD? 1 2 3 4

Answer 1

The correct option is 3.

Explanation:

The vertices of figure ABCD are (-5,5), (-5,2),(-3,1) and (-3,3).

Translation is a rigid transformation, it means the size and shape of the image and preimage are same, and the figure shifts from one place to another without making any changes.

The translation of a figure it defined as

`(x,y)\rightarrow (x+a,y+b)`

where, a is horizontal shift and b is vertical shift.

Only figure 3 represent the shift in given figure. The rule of translation is

`(x,y)\rightarrow (x+6,y-4)`

`(-5,5)\rightarrow (-5+6,5-4)=(1,1)`

`(-5,2)\rightarrow (-5+6,2-4)=(1,-2)`

`(-3,1)\rightarrow (-3+6,1-4)=(3,-3)`

`(-3,3)\rightarrow (-3+6,3-4)=(3,-1)`

These are the coordinates of figure 3.

Therefore the correct option is 3.

Answer 2

Figure 3 (with endpoints 1, 1; 1, -2; 3, -1; and 3, -3) is the translation of polygon ABCD.

The x and y coordinates of ABCD (with endpoints -5, 5; -5, 2; -3, 1 and -3, 3) have been moved by a fixed distance (6 units towards the right and 4 units downwards in this case)