ValentinaT
What is the length of the longest side of a triangle that has vertices at (5, 2) (1,6) and (1,2)?



This Question is Closed

v4xN0s
Best Response
You've already chosen the best response.
0
Use the distance formula

ValentinaT
Best Response
You've already chosen the best response.
1
Distance formula?

v4xN0s
Best Response
You've already chosen the best response.
0
LOL

v4xN0s
Best Response
You've already chosen the best response.
0
ok its \[d=\sqrt{(x _{1}x _{2})^2+(y _{1}y _{2})^2} \]

MathLegend
Best Response
You've already chosen the best response.
5
I would also suggest labeling your coordinates

v4xN0s
Best Response
You've already chosen the best response.
0
MathLegend ur not a math legend at all

MathLegend
Best Response
You've already chosen the best response.
5
A= (5, 2)
B = (1,6)
C = (1,2)

MathLegend
Best Response
You've already chosen the best response.
5
So when using the distance formula... you can solve for side AB first.

ValentinaT
Best Response
You've already chosen the best response.
1
Thank you.

MathLegend
Best Response
You've already chosen the best response.
5
So using that formula, can you label the coordinates as (x1, y1) & (x2,y2)

hba
Best Response
You've already chosen the best response.
0
dw:1355599903259:dw

MathLegend
Best Response
You've already chosen the best response.
5
A= (5, 2)
B = (1,6)
So lets solve for side AB first... so, "A" comes first right? So let that be your x1 & y1
Then, "B" can be your x2 & y2

MathLegend
Best Response
You've already chosen the best response.
5
Do you understand so far @ValentinaT ?

MathLegend
Best Response
You've already chosen the best response.
5
All I did was label them so that we can plug it into that distance formula.

MathLegend
Best Response
You've already chosen the best response.
5
@ValentinaT let me know when you get back so we can work this out together. :)

ValentinaT
Best Response
You've already chosen the best response.
1
Yeah, I'm getting it, thank you.

ValentinaT
Best Response
You've already chosen the best response.
1
\[\frac{ 6  2 }{ 5  1 } = \frac{ 8 }{ 6}\]

MathLegend
Best Response
You've already chosen the best response.
5
So for AB
(1+5)^2+(62)^2

MathLegend
Best Response
You've already chosen the best response.
5
I'm sorry the formula is actually x2x1 and y2y1 the above poster just mixed up the two.

ValentinaT
Best Response
You've already chosen the best response.
1
Okay.

MathLegend
Best Response
You've already chosen the best response.
5
(1+5)^2+(62)^2
(6)^2+(8)^2
36+64

MathLegend
Best Response
You've already chosen the best response.
5
36+64 = 100

MathLegend
Best Response
You've already chosen the best response.
5
\[\sqrt{100}\]

ValentinaT
Best Response
You've already chosen the best response.
1
10

MathLegend
Best Response
You've already chosen the best response.
5
Now, we need the square root... because if you notice that entire formula had the square root symbol over it

MathLegend
Best Response
You've already chosen the best response.
5
Good.

MathLegend
Best Response
You've already chosen the best response.
5
So side AB = 10

MathLegend
Best Response
You've already chosen the best response.
5
So that is one side. So lets go for side BC

MathLegend
Best Response
You've already chosen the best response.
5
B = (1,6)
x1 y1
C = (1,2)
x2 y2

MathLegend
Best Response
You've already chosen the best response.
5
@ValentinaT do you feel comfortable trying it out on your own? Tell me what you get and I'll check to see if your answer for side BC is correct.

ValentinaT
Best Response
You've already chosen the best response.
1
\[\frac{ 2  6 }{ 1  1 } = \frac{ 8 }{ 0 }\]

MathLegend
Best Response
You've already chosen the best response.
5
Remember we are not trying to find a slope.

MathLegend
Best Response
You've already chosen the best response.
5
We are looking for the distance between the vertices.

MathLegend
Best Response
You've already chosen the best response.
5
(11)^2 + (2+6)^2

MathLegend
Best Response
You've already chosen the best response.
5
To get that all I did was plug it into the formula.
(x2x1)^2+(y2y1)^2

MathLegend
Best Response
You've already chosen the best response.
5
(11)^2 + (2+6)^2
Try solving that.

ValentinaT
Best Response
You've already chosen the best response.
1
Okay, 0 + 64?

MathLegend
Best Response
You've already chosen the best response.
5
Good

MathLegend
Best Response
You've already chosen the best response.
5
0 + 64 = 64
\[\sqrt{64}\]

ValentinaT
Best Response
You've already chosen the best response.
1
So, 8 as the square root.

MathLegend
Best Response
You've already chosen the best response.
5
Yes, so side BC = 8

MathLegend
Best Response
You've already chosen the best response.
5
Now, try side AC

MathLegend
Best Response
You've already chosen the best response.
5
(x2x1)^2+(y2y1)^2

ValentinaT
Best Response
You've already chosen the best response.
1
A = 5, 2 = x1, y1
C = 1, 2 = x2, y2
\[\frac{ 1  5^2}{ 2  2^2 } = \frac{ 6 }{ 1 } \] so 36?

MathLegend
Best Response
You've already chosen the best response.
5
(x2x1)^2+(y2y1)^2
(1+5)^2 + (22)^2 Do you understand this step?

ValentinaT
Best Response
You've already chosen the best response.
1
36 + 0 Yeah I get it, I just couldn't figure out how to write it.

MathLegend
Best Response
You've already chosen the best response.
5
Good so if you took the square root of 36
\[\sqrt{36}\]

MathLegend
Best Response
You've already chosen the best response.
5
So now, we know the length of the longest side is AB

ValentinaT
Best Response
You've already chosen the best response.
1
Okay, thank you!