Question

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

Answer 1

what formula should be used to find this ?

Answer 2

@dumbcow

Answer 3

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

Answer 4

using the slope formula ?

Answer 5

Pythagoras theorem : c^2 = a^2 + b^2

Answer 6

its an equilateral triangle

Answer 7

all the sides are equal ?

Answer 8

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

Answer 9

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

Answer 10

yes

Answer 11

so calculate
AB=?
AC=?
BC=?

Answer 12

AB - 13
BC - 13
CA - 26

Answer 13

so its a right ?

Answer 14

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

Answer 15

yea

Answer 16

so let's see if it's right

is CA^2 = AB^2 + BC^2 ?

Answer 17

no

Answer 18

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

Answer 19

jk yes haha

Answer 20

CA^2 = ?

Answer 21

26 and @phi looks like a right

Answer 22

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

Answer 23

which r the two lines that form the right angle?

Answer 24

lines AB and BC

Answer 25

the slopes dont match

-1.5 and 0.66666667

Answer 26

-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*

Answer 27

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