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- anonymous

I need help with this. Can anyone assist me?
Quadrilateral FGHI is shown on the coordinate plane with coordinates F at 4, −2; G at 7, −2; H at 5, −4; and I 2, −4. Point A is at −2, 7 and point D is at −10, −1.
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 (−2, 7) and point D (−10, −1), what is another point that could represent point B?

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- anonymous

- schrodinger

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- iwillrektyou

I believe you need to use the distance formula for this.

- anonymous

And what exactly is that. I am clueless

- iwillrektyou

Do they lie on the same line (colinear)?

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- iwillrektyou

And the distance formula is \[\sqrt{(x2 - x1)^2 + (y2 - y1)^2)}\]

- anonymous

Yes they are colinear.

- iwillrektyou

Alright. So just substitute the points for x1, x2, y1, and y2. I will guide you through this.

- iwillrektyou

\[\sqrt{(-10 + 2)^2 + (-1 - 7)^2}\]

- anonymous

is the answer (12, 7)

- iwillrektyou

\[\sqrt{(-8)^2 + (-8)^2)}\]

- iwillrektyou

\[\sqrt{64 + 64}\]

- iwillrektyou

\[\sqrt{128} = \]

- iwillrektyou

11.31

- anonymous

Oh wow. This is really helpful. Thanks

- iwillrektyou

So 11.31 is the distance between A and D.
Is this quadrilateral a square or..?

- anonymous

a square

- iwillrektyou

Ok good! That makes it so much easier.

- anonymous

So the answer options were
a. (14,7)
b. (10,7)
c. (12,7)
d, (8,7 )

- iwillrektyou

Also, the points must match, so it would be A = F, B = G, C = H, D = I

- iwillrektyou

\[\sqrt{(-2 - x1)^2 + (7 - y1)^2}\]

- iwillrektyou

The answer is either b or c.

- anonymous

I got c.

- iwillrektyou

Ok great job!

- anonymous

Thank you

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