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In the xy-plane, what is the perimeter of the triangle with vertices a

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In the xy-plane, what is the perimeter of the triangle with vertices a [#permalink] New post   04 Jan 2023, 12:13
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In the 𝑥𝑦-plane, what is the perimeter of the triangle with vertices at (0, 0), (3, 4), and (−1, 7)?

(A) 25
(B) \(4 \sqrt{5}\)
(C) \(10 + 5 \sqrt{2}\)
(D) \(10 + 3 \sqrt{7}\)
(E) \(5 + 10 \sqrt{2}\)
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In the xy-plane, what is the perimeter of the triangle with vertices a [#permalink] New post   04 Jan 2023, 14:51
Kushchokhani wrote:
In the 𝑥𝑦-plane, what is the perimeter of the triangle with vertices at (0, 0), (3, 4), and (−1, 7)?

(A) 25
(B) \(4 \sqrt{5}\)
(C) \(10 + 5 \sqrt{2}\)
(D) \(10 + 3 \sqrt{7}\)
(E) \(5 + 10 \sqrt{2}\)


We can find the distance, d, between \((x_1,y_1)\) and \((x_2,y_2)\) using the equation

\(d = \sqrt{(x_1-x_2)^2 + (y_1-y_2)^2}\)

This will help get the distance between each of the points, thereby get the length of each side of the triangle.

Once the length is obtained, the same can be added to get the perimeter.

Option C
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Re: In the xy-plane, what is the perimeter of the triangle with vertices a [#permalink] New post   04 Jan 2023, 22:44
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Kushchokhani wrote:
In the 𝑥𝑦-plane, what is the perimeter of the triangle with vertices at (0, 0), (3, 4), and (−1, 7)?

(A) 25
(B) \(4 \sqrt{5}\)
(C) \(10 + 5 \sqrt{2}\)
(D) \(10 + 3 \sqrt{7}\)
(E) \(5 + 10 \sqrt{2}\)


Solution:

  • We are asked about the perimeter of the triangle with vertices A(0, 0), B(3, 4), and C(−1, 7)
  • Length of \(AB=\sqrt{(3-0)^2+(4-0)^2}=\sqrt{9+16}=\sqrt{25}=5\)
  • Length of \(BC=\sqrt{(-1-3)^2+(7-4)^2}=\sqrt{16+9}=\sqrt{25}=5\)
  • Length of \(CA=\sqrt{(-1-0)^2+(7-0)^2}=\sqrt{1+49}=\sqrt{50}\)
  • Perimeter \(=AB+BC+CA=5+5+\sqrt{50}=10+\sqrt{50}=10+5\sqrt{2}\)

Hence the right answer is Option C
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Re: In the xy-plane, what is the perimeter of the triangle with vertices a [#permalink]
04 Jan 2023, 22:44
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