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ValentinaT

  • 2 years ago

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

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  1. v4xN0s
    • 2 years ago
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    Use the distance formula

  2. ValentinaT
    • 2 years ago
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    Distance formula?

  3. v4xN0s
    • 2 years ago
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    LOL

  4. v4xN0s
    • 2 years ago
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    ok its \[d=\sqrt{(x _{1}-x _{2})^2+(y _{1}-y _{2})^2} \]

  5. MathLegend
    • 2 years ago
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    I would also suggest labeling your coordinates

  6. v4xN0s
    • 2 years ago
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    MathLegend ur not a math legend at all

  7. MathLegend
    • 2 years ago
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    A= (-5, 2) B = (1,-6) C = (1,2)

  8. MathLegend
    • 2 years ago
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    So when using the distance formula... you can solve for side AB first.

  9. ValentinaT
    • 2 years ago
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    Thank you.

  10. MathLegend
    • 2 years ago
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    So using that formula, can you label the coordinates as (x1, y1) & (x2,y2)

  11. hba
    • 2 years ago
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    |dw:1355599903259:dw|

  12. MathLegend
    • 2 years ago
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    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

  13. MathLegend
    • 2 years ago
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    Do you understand so far @ValentinaT ?

  14. MathLegend
    • 2 years ago
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    All I did was label them so that we can plug it into that distance formula.

  15. MathLegend
    • 2 years ago
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    @ValentinaT let me know when you get back so we can work this out together. :)

  16. ValentinaT
    • 2 years ago
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    Yeah, I'm getting it, thank you.

  17. ValentinaT
    • 2 years ago
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    \[\frac{ -6 - 2 }{ -5 - 1 } = \frac{ -8 }{ -6}\]

  18. MathLegend
    • 2 years ago
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    So for AB (1+5)^2+(-6-2)^2

  19. MathLegend
    • 2 years ago
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    I'm sorry the formula is actually x2-x1 and y2-y1 the above poster just mixed up the two.

  20. ValentinaT
    • 2 years ago
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    Okay.

  21. MathLegend
    • 2 years ago
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    (1+5)^2+(-6-2)^2 (6)^2+(-8)^2 36+64

  22. MathLegend
    • 2 years ago
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    36+64 = 100

  23. MathLegend
    • 2 years ago
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    \[\sqrt{100}\]

  24. ValentinaT
    • 2 years ago
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    10

  25. MathLegend
    • 2 years ago
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    Now, we need the square root... because if you notice that entire formula had the square root symbol over it

  26. MathLegend
    • 2 years ago
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    Good.

  27. MathLegend
    • 2 years ago
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    So side AB = 10

  28. MathLegend
    • 2 years ago
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    So that is one side. So lets go for side BC

  29. MathLegend
    • 2 years ago
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    B = (1,-6) x1 y1 C = (1,2) x2 y2

  30. MathLegend
    • 2 years ago
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    @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.

  31. ValentinaT
    • 2 years ago
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    \[\frac{ 2 - -6 }{ 1 - 1 } = \frac{ 8 }{ 0 }\]

  32. MathLegend
    • 2 years ago
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    Remember we are not trying to find a slope.

  33. MathLegend
    • 2 years ago
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    We are looking for the distance between the vertices.

  34. MathLegend
    • 2 years ago
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    (1-1)^2 + (2+6)^2

  35. MathLegend
    • 2 years ago
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    To get that all I did was plug it into the formula. (x2-x1)^2+(y2-y1)^2

  36. MathLegend
    • 2 years ago
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    (1-1)^2 + (2+6)^2 Try solving that.

  37. ValentinaT
    • 2 years ago
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    Okay, 0 + 64?

  38. MathLegend
    • 2 years ago
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    Good

  39. MathLegend
    • 2 years ago
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    0 + 64 = 64 \[\sqrt{64}\]

  40. ValentinaT
    • 2 years ago
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    So, 8 as the square root.

  41. MathLegend
    • 2 years ago
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    Yes, so side BC = 8

  42. MathLegend
    • 2 years ago
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    Now, try side AC

  43. MathLegend
    • 2 years ago
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    (x2-x1)^2+(y2-y1)^2

  44. ValentinaT
    • 2 years ago
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    A = -5, 2 = x1, y1 C = 1, 2 = x2, y2 \[\frac{ 1 - -5^2}{ 2 - 2^2 } = \frac{ 6 }{ 1 } \] so 36?

  45. MathLegend
    • 2 years ago
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    (x2-x1)^2+(y2-y1)^2 (1+5)^2 + (2-2)^2 Do you understand this step?

  46. ValentinaT
    • 2 years ago
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    36 + 0 Yeah I get it, I just couldn't figure out how to write it.

  47. MathLegend
    • 2 years ago
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    Good so if you took the square root of 36 \[\sqrt{36}\]

  48. MathLegend
    • 2 years ago
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    So now, we know the length of the longest side is AB

  49. ValentinaT
    • 2 years ago
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    Okay, thank you!

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