Question

Parallelogram FGHI on the coordinate plane below represents the drawing of a horse trail through a local park: 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 (0, 4) and point D (−6, −5), what is another point that could represent point C?

A-(9,-5)
B-(6,-5)
C-(12,-5)
D-(3,-5)

Answer 1

(6,-5)

Explanation:

Answer 2

Let's check the scaling of the direction vectors, the difference between the points. We'll assume FI is mapped to AD.

F - I=(-6 - -8, 6 - 3) = (2,3)

A - D = (0 - - 6, 4 - -5) = (6,9)

We see A-D=3(F-I); that is, we're dealing with a scale factor of 3.

FG is 4 units long so AB will be 4(3)=12 units long.

All the choices have positive x so we don't have to worry about the possibiity that the big parallelogram is all to the left of the y axis.

B=A+(12,0)=(12,4)

C=D+(12,0)=(6,-5)

Reviewing the choices we get

Answer: B