Parallelogram fghi on the coordinate plane below represents the drawing of a horse trail through a local park: quadrilateral fghi is shown on the coordinate plane with coordinates f at −6, −1; g at −1, −1; h at −2, −4; and i −7, −4. point a is at 3, 8 and point d is at 1, 2. in order to build a scale model of the trail, the drawing is enlarged as parallelogram abcd on the coordinate plane. if two corners of the trail are at point a (3, 8) and point d (1, 2), what is another point that could represent point b? (10, 8) (13, 8) (8, 8) (6, 8)

we know that

 Parallelogram is a quadrilateral with opposite sides parallel and equal in length

so

we have

Step 1

Find the distance FI

we know that

the distance between two points is equal to the formula

substitute the values

Step 2

Find the distance FG

we know that

the distance between two points is equal to the formula

substitute the values

Step 3

Find the distance AD

we know that

the distance between two points is equal to the formula

substitute the values

Step 4

Find the scale factor

we know that

the scale factor is equal to

we have

substitute the values

Step 5

Find the coordinate of point B

we know that

the length side of the segment AB is equal to

we have

substitutes

the x-coordinate of point B is equal to the x-coordinate of point A plus the distance AB

where

Bx------> is the x-coordinate of point B

Ax-------> is the x-coordinate of point A

dAB------> distance AB

susbtitute

the y-coordinate of point B is equal to the y-coordinate of point A

therefore

the coordinate of point B is

the answer is the option