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