Question

The coordinates J(2, 2), K(-1, 3), L(-2, -1) form a right triangle. true or false

Answer 1

@jim_thompson5910

Answer 2

Plot the points. Then use the distance formula. If the Pythagorean theorem holds, then it's a right triangle.

Answer 3

i dont have anything to plot them on

Answer 4

\[d=\sqrt{\Delta x ^{2}+\Delta y ^{2}}\]

Answer 5

you need to use the distance formula to find the segments

JK
KL
JL

Answer 6

if you can show that

a^2 + b^2 = c^2

is true, where a,b,c are the 3 side lengths and c is the longest side, then the triangle is a right triangle

Answer 7

so its kinda long process to find im guessing okayyyyyyy here we go

Answer 8

yes it's quite long since you need to use the formula hairynmad gave you to find JK, KL and JL

Answer 9

once you have those 3 sides, you plug them into a^2 + b^2 = c^2 to test if it's a right triangle or not

Answer 10

can you help e set up the first one just to make sure im doing it right

Answer 11

which side length do you want to find

JK
KL
JL

??

Answer 12

jk

Answer 13

is the answer to it sqrt10

Answer 14

?

Answer 15

yes

Answer 16

okay so after i get all those answers how do i plug them into the a2+b2=c2?

Answer 17

like does it matter where i place them in the equation?

Answer 18

false

Answer 19

longest side will be c, the hypotenuse
the other two, the legs, don't matter, can be either a or b

Answer 20

as long as c is the longest side, everything else doesn't matter

Answer 21

okay gotcha . so is it sqrt10 or no?

Answer 22

correct, JK = sqrt(10)

Answer 23

okay

Answer 24

sooooo this is what i got

Answer 25

sqrt10^2+ sqrt17 ^2 = sqrt25^2

Answer 26

hwo the heck do i work that out

Answer 27

one sec while I check

Answer 28

i got false it is not a right triangle am i right?

Answer 29

okay

Answer 30

KL = sqrt(17)

that's correct

Answer 31

JL = sqrt(25) which is really just 5

so

JL = 5

Answer 32

a^2 + b^2 = c^2

(JK)^2 + (KL)^2 = (JL)^2

(sqrt(10))^2 + (sqrt(17))^2 = (5)^2

10 + 17 = 25

27 = 25

This is FALSE, so a^2 + b^2 = c^2 is FALSE when

a = sqrt(10)
b = sqrt(17)
c = 5

Answer 33

so yes, you're correct

this isn't a right triangle

Answer 34

okay wow that really helps i appreciate the help both of you so much

Answer 35

you're welcome