Question

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

http://prntscr.com/8w37bm

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)

Answer 1

@jim_thompson5910

Answer 2

what is the slope of segment FI ?

Answer 3

I forget how to find that.

Answer 4

slope = rise/run

Answer 5

going from F to I, what is the rise? what is the run?

Answer 6

Isn't there an x and y formula for slope? I learned that last year, but can't remember it.

Answer 7

yes

\[\Large m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}\]

Answer 8

I only ask because I never could get a hold of the rise and run concept.

Answer 9

subtract the y coordinates
subtract the x coordinates in the same order
divide the y difference over the x difference

Answer 10

From that, I got -3 over -1. Is that right?

Answer 11

-3 over -1 reduces to +3

Answer 12

Okay.

Answer 13

So the slope is 3

Answer 14

see attached as to how you would do this with rise/run

Answer 15

Okay, that should help for the future.

Answer 16

now tell me what the slope is for the line segment that goes through D and A

Answer 17

-6 over -2
could that simplify?

Answer 18

yes, -6 divided by -2 = +3

Answer 19

so we see the slope is the same

Answer 20

notice how the rise for FI was 3
the rise for DA is 6

this means we have a scale factor of 2 (3 doubles to 6)

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the run for FI is 1
the run for DA is 2

again, the scale factor is 2

Answer 21

F and G are 5 units apart

so A and B are going to be 10 units apart (doubled 5 to get 10)