## Gabylovesyou one year ago If A = (1, 4) B = (3, 1) and C = (6, 3), classify the the following triangle as either equilateral or right. Type the word equilateral or right in the blank. @ganeshie8

1. Gabylovesyou

what formula should be used to find this ?

2. Gabylovesyou

@dumbcow

3. hoblos

try calculating the length of the 3 sides if they are equal, it would be equilateral if not, you have to check if they apply Pythagoras theorem

4. Gabylovesyou

using the slope formula ?

5. hoblos

|dw:1396980676890:dw| Pythagoras theorem : c^2 = a^2 + b^2

6. Gabylovesyou

its an equilateral triangle

7. hoblos

all the sides are equal ?

8. Gabylovesyou

wait no i think its a right ;/ idk ..

9. hoblos

do you know how to calculate the distance between two points ?

10. Gabylovesyou

yes

11. hoblos

so calculate AB=? AC=? BC=?

12. Gabylovesyou

AB - 13 BC - 13 CA - 26

13. Gabylovesyou

so its a right ?

14. hoblos

they are actually AB = √13 BC = √13 CA = √26 right ?

15. Gabylovesyou

yea

16. hoblos

so let's see if it's right is CA^2 = AB^2 + BC^2 ?

17. Gabylovesyou

no

18. phi

I would plot it. If the choice is either equilateral or right triangle, you can tell by eyeball

19. Gabylovesyou

jk yes haha

20. hoblos

CA^2 = ?

21. Gabylovesyou

26 and @phi looks like a right

22. phi

If you want to prove it, find the lengths if each side and show pythagoras works or find the slope of the two lines that form the right angle and see if the slopes are negative reciprocals

23. Gabylovesyou

which r the two lines that form the right angle?

24. phi

lines AB and BC

25. Gabylovesyou

the slopes dont match -1.5 and 0.66666667

26. phi

-3/2 and ⅔ it's easier to see if you multiply one by -1 and then flip it, you get the other *negative reciprocals*

27. phi

which means the lines are perpendicular (form a 90º angle) so you have proven its a right triangle.