Question

done/got help

Answer 1

you have to find the slope of all three segments

Answer 2

@acxbox22 what do you mean? also please read my question again i redid something i did wrong the first time.

Answer 3

you made an error with the first slope

Answer 4

the slope formula is

m = (y2-y1)/(x2-x1)

the y difference is on top, the x difference is down below

Answer 5

but you mixed up x and y for that first slope

Answer 6

Yeah I know and Ohhh I see thanks Jim give me a sec to redo!

Answer 7

well use the formula above to find the slope of all three segments made by the three points
then we examine the slopes
out of the three slopes if two are perpendicular slopes than it is a right triangle

Answer 8

oh wait, nvm, I misread

the only error you made on the first one is that the slope is actually +0.2 and not -0.2

Answer 9

in any event, the two slopes don't multiply to -1

0.2*(-4) = -0.8

so the two lines are NOT perpendicular

Answer 10

So it is not a right triangle?
So I did that part correctly?

Answer 11

you need to show that the other pairs of segments aren't perpendicular

Answer 12

yes

Answer 13

other pair of segments? so I need to find the slope between (2,2) and (6,7)?

Answer 14

X(2,2)
Y(6,7)
Z(7,3)


you found the slope of line YZ to be -4
you found the slope of line XZ to be 0.2

Answer 15

find the slope of XY and use it to see if XY is perpendicular to either YZ or XZ

Answer 16

Ahhh okay I see now! give me a sec okay?

Answer 17

sure

Answer 18

oops ignore the first K idk why its their lol

Answer 19

slope of line YZ is -4
slope of line XZ is 0.2
slope of line XY is 1.25

Answer 20

let

m1 = slope of YZ
m2 = slope of XZ
m3 = slope of XY

if

m1*m2 = -1
or
m1*m3 = -1
or
m2*m3 = -1

if any of the above statements are true, then we have a pair of perpendicular lines

Answer 21

looks good

Answer 22

none of those results are -1, so we don't have a right triangle

Answer 23

Btw thanks for having patience with me and making this easy :]
Alright so now I have to figure out what changes could be made to make it a right triangle.

Answer 24

hmm let me think

Answer 25

Could changing the coordinates work?

Answer 26

yes it turns out that all you need to do is move 1 point

Answer 27

there are infinitely many ways to do this, but one way is to move point Y up one unit. Recompute the slopes and confirm that you do indeed get a pair of perpendicular lines.

Answer 28

X(2,2)
Y(6,7) ---> turns into Y(6,8)
Z(7,3)

compute the slopes of XY, XZ, YZ

Answer 29

you made an error here

YZ = 8-4/6-7 = 4/-1 = - 4

Answer 30

I don't know where you got the 4 in "8-4/6-7"

Answer 31

I made X and Z stay where they are. I only moved Y

Answer 32

anything involving point Z

Answer 33

multiply those slopes and see which multiply to -1

Answer 34

so XZ and YZ are perpendicular, making a right angle occur at their intersection point

Answer 35

yay awesome! Is this it? Did we really work out the whole problem? lol sorry my head actually hurts from all this but I am truly thankful for your help it was amazing and you were very patient and made me understand this which is beyond amazing! Thank you.

Answer 36

yeah that's the full thing and I'm glad it's all making sense now