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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

Geometry
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what formula should be used to find this ?
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

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Other answers:

using the slope formula ?
|dw:1396980676890:dw| Pythagoras theorem : c^2 = a^2 + b^2
its an equilateral triangle
all the sides are equal ?
wait no i think its a right ;/ idk ..
do you know how to calculate the distance between two points ?
yes
so calculate AB=? AC=? BC=?
AB - 13 BC - 13 CA - 26
so its a right ?
they are actually AB = √13 BC = √13 CA = √26 right ?
yea
so let's see if it's right is CA^2 = AB^2 + BC^2 ?
no
  • phi
I would plot it. If the choice is either equilateral or right triangle, you can tell by eyeball
1 Attachment
jk yes haha
CA^2 = ?
26 and @phi looks like a right
  • 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
which r the two lines that form the right angle?
  • phi
lines AB and BC
the slopes dont match -1.5 and 0.66666667
  • 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*
  • phi
which means the lines are perpendicular (form a 90º angle) so you have proven its a right triangle.

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