## anonymous one year ago 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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1. iwillrektyou

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

2. anonymous

And what exactly is that. I am clueless

3. iwillrektyou

Do they lie on the same line (colinear)?

4. iwillrektyou

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

5. anonymous

Yes they are colinear.

6. iwillrektyou

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

7. iwillrektyou

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

8. anonymous

9. iwillrektyou

$\sqrt{(-8)^2 + (-8)^2)}$

10. iwillrektyou

$\sqrt{64 + 64}$

11. iwillrektyou

$\sqrt{128} =$

12. iwillrektyou

11.31

13. anonymous

Oh wow. This is really helpful. Thanks

14. iwillrektyou

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

15. anonymous

a square

16. iwillrektyou

Ok good! That makes it so much easier.

17. anonymous

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

18. iwillrektyou

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

19. iwillrektyou

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

20. iwillrektyou

The answer is either b or c.

21. anonymous

I got c.

22. iwillrektyou

Ok great job!

23. anonymous

Thank you