Question

Determine if triangle RST with coordinates R (3,4), S (5,5) and T (6,1)
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

find slope by formula
\[m=\frac{ y _{2}-y _{1} }{x _{2}-x _{1}}\]
taking two points at a time and see if m1*m2=-1

Answer 2

So I have to figure out if all possibilities of those points when subtracted equal to -1?

Answer 3

slope of RS
\[m _{1}=\frac{ 5-4 }{ 5-3 }=\frac{ 1 }{ 2 }\]

Answer 4

slope of RT
\[m _{2}=\frac{ 1-4 }{ 6-3 }=\frac{ -3 }{ 3 }=-1\]

Answer 5

slope of ST
\[m _{3}=\frac{ 1-5 }{ 6-5 }=\frac{ -4 }{ 1 }=-4\]

Answer 6

Now I see what you mean. This was very helpful.

Answer 7

So I would say that RS and ST need to equal -1 for it to be a right triangle?

Answer 8

Am I right? I will give you best answer.

Answer 9

product of any two should be -1
which is not the case
so change co-ordinates of one point to make the product -1

Answer 10

Product of any two? Okay you saved me there. Thank you very much.

Answer 11

Can you help me with another one?

Answer 12

adjust the coordinates

Answer 13

2. find the slopes of CB and FE

Answer 14

For line FE I got -4/-5 and for line CB I got -3/-4

Answer 15

How do I know if they are opposite and reciprocal?

Answer 16

slope of FE
\[=\frac{ -4-(-1) }{ 5-1 }=\frac{ -3 }{ 4 }\]
slope of CB
\[=\frac{ 5-1 }{ 4-1 }=\frac{ 4 }{ 3 }\]