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tiny-mole [99]
3 years ago
7

Find ST if S(-3, 10) and T(-2, 3).

Mathematics
1 answer:
8090 [49]3 years ago
4 0

Answer:

ST = 5\sqrt{2}

Step-by-step explanation:

Given:

S(-3, 10)

T(-2, 3)

Required:

ST

SOLUTION:

Use the distance formula, \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}, to find ST.

Where,

S(-3, 10) = (x_1, y_1)

T(-2, 3) = (x_2, y_2)

ST = \sqrt{(-2 -(-3))^2 + (3 - 10)^2}

ST = \sqrt{(1)^2 + (-7)^2}

= \sqrt{1 + 49}

= \sqrt{50} = \sqrt{25*2}

ST = 5\sqrt{2}

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4 0
3 years ago
Triangle JKL has vertices J(2,5), K(1,1), and L(5,2). Triangle QNP has vertices Q(-4,4), N(-3,0), and P(-7,1). Is (triangle)JKL
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Answer:

Yes they are

Step-by-step explanation:

In the triangle JKL, the sides can be calculated as following:

  • J(2;5); K(1;1)

             => JK = \sqrt{(1-2)^{2} + (1-5)^{2}  } = \sqrt{(-1)^{2}+(-4)^{2}  } = \sqrt{1+16}=\sqrt{17}

  • J(2;5); L(5;2)

             => JL = \sqrt{(5-2)^{2} + (2-5)^{2}  } = \sqrt{3^{2}+(-3)^{2}  } = \sqrt{9+9}=\sqrt{18} = 3\sqrt{2}

  • K(1;1); L(5;2)

             =>  KL = \sqrt{(5-1)^{2} + (2-1)^{2}  } = \sqrt{4^{2}+1^{2}  } = \sqrt{1+16}=\sqrt{17}

In the triangle QNP, the sides can be calculate as following:

  • Q(-4;4); N(-3;0)

             => QN = \sqrt{[-3-(-4)]^{2} + (0-4)^{2}  } = \sqrt{1^{2}+(-4)^{2}  } = \sqrt{1+16}=\sqrt{17}

  • Q (-4;4); P(-7;1)

   => QP = \sqrt{[-7-(-4)]^{2} + (1-4)^{2}  } = \sqrt{(-3)^{2}+(-3)^{2}  } = \sqrt{9+9}=\sqrt{18} = 3\sqrt{2}

  • N(-3;0); P(-7;1)

             =>  NP = \sqrt{[-7-(-3)]^{2} + (1-0)^{2}  } = \sqrt{(-4)^{2}+1^{2}  } = \sqrt{16+1}=\sqrt{17}

It can be seen that QPN and JKL have: JK = QN; JL = QP; KL = NP

=> They are congruent triangles

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