Question

Parallelogram FGHI on the coordinate plane below represents the drawing of a horse trail through a local park: (Via Image)

In order to build a scale model of the trail, the drawing is enlarged on the coordinate plane. If two corners of the trail are at point A(0, 4) and point D(−6, −5), what is another point that could represent a corner of the trail?
1) (4, 4)
2) (11, 4)
3) (6, −5)
4) (−17, −5)

Answer 1

The answer is (6,-5)
This is because the scale between the drawing and the new model is 3.
The only point that matches the new scale is (6,-5)
I'm sorry if this explanation is confusing but I hope it helps.

Answer 2

Correct choice is 3)

Explanation:

Enlargment is a dilation. A dilation is a transformation that preserves parallel lines and each side length of the pre-image parallelogram is multiplied by the same coefficient.

Note that

`\overrightarrow{IF}=(-7-(-9),5-2)=(2,3);\\ \\\overrightarrow{DA}=(0-(-6),4-(-5))=(6,9)=3\cdot (2,3)=3\overrightarrow{IF}.`

From this statement you can conclude that the factor of dilation is 3.

Since

`\overrightarrow{FG}=(-3-(-7),5-5)=(4,0),`

then

`\overrightarrow{AB}=3\overrightarrow{FG}=3(4,0)=(12,0)\ \text{or}\ \overrightarrow{BA}=(12,0)`

and

`\overrightarrow{DC}=(12,0)\ \text{or}\ \overrightarrow{CD}=(12,0)`

Yhis gives you that B(12,4) (or B(-12,4)) and C(6,-5) (or C(-18,-5)).