Question

Determine if triangle XYZ with coordinates X (2, 2), Y (6, 7), and Z (7, 3) is a right triangle. Use evidence to support your claim. If it is not a right triangle, what changes can be made to make it a right triangle? Be specific.

Answer 1

There are 2 ways I can suggest:

First work out the length of all the sides (using the coordinates of the endpoints).

Then call the 2 shorter sides a & b , and the other one c

if a^2 +b^2 = c^2 then it is a right angle (by Pythagoras)

second -

Work out the slope of XZ (m1)
Work out the slope of YZ (m2)

if the they are perpendicular then m1- -1/m2

Answer 2

cani show you what i got?

Answer 3

We first must use the distance formula to find out if the distance fits in to the Pythagorean theorem.
Distance formula:
Sqrt{(x2 - x1)^2 + (y2 - y1)^2}
so we now plug in the coordinates to find distance of X to Y.
Sqrt{(6 - 2)^2 + (7-2)^2}
Sqrt{(4)^2 + (5)^2}
Sqrt{16 + 25}
Sqrt{41}
Now find distance for Y to Z
Sqrt{(7 - 6)^2 + (3 - 7)^2}
Sqrt{(1)^2 + (-4)^2}
Sqrt{1+ -16}
Sqrt{-15}
Now find distance for X to Z
Sqrt{(7 - 2)^2 + (3 - 2)^2}
Sqrt{(5)^2 + (1)^2}
Sqrt{25 + 1}
Sqrt{26}
So now we add 26 and -15 to see if it adds up to XY distance.
26 - 15 = 11
So since 11 is not equal 41, then this triangle is not a right triangle.

Answer 4

I meant m1=-1/m2

Answer 5

and to fix it, all that is needed is make the 3 in point Z a -3

Answer 6

@hartnn

Answer 7

you have made a mistake with your lengths (YZ)

Your method is fine, but the calculation is wrong

Answer 8

Sqrt{(7 - 6)^2 + (3 - 7)^2}
Sqrt{(1)^2 + (-4)^2}
Sqrt{1+ -16} <--here?
Sqrt{-15}

Answer 9

should it be 16 not -16

Answer 10

That is not correct
Yes -4^2 = 16

Answer 11

yes - you are correct now

Answer 12

ah ok so
Now find distance for Y to Z
Sqrt{(7 - 6)^2 + (3 - 7)^2}
Sqrt{(1)^2 + (-4)^2}
Sqrt{1+16}
Sqrt{17}
17 + 26 still does not equal 41

Answer 13

correct

Answer 14

ah thanks, what about the second part of the question?

Answer 15

soz - gtg

Answer 16

soz?

Answer 17

ok thanks bye

Answer 18

the easy solution is find the slope of the 3 segments. Multiply the slopes of each pair. If the answer from the multiplication is -1 then the lines are perpendicular.

Answer 19

ah ok that is easier

Answer 20

can you help me with the second part of the question?
If it is not a right triangle, what changes can be made to make it a right triangle? Be specific.

Answer 21

for the adjustment, take the slope of a line segment. then for the other segment adjust an endpoint so the the slope is the negative reciprocal of the slope you started with.

Answer 22

ok but i would have to restart right? since i didn't do the slope way

Answer 23

@campbell_st

Answer 24

nvm i got it

Answer 25

thanks to the both of you