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Vinil7 [7]
3 years ago
9

REALLY IMPORTANT

Mathematics
1 answer:
Mashutka [201]3 years ago
7 0

Answer:

we choose (3,4)

Step-by-step explanation:

Given the coordinates:

  • A (5, 2)
  • B (5, -2)
  • C  (2,1)
  • L (-5, 6)
  • M (-5, -6)

To find a distance between two points or the length of the segment, we use the following formula:

\sqrt{(x2-x1)^2+(y2-y1)^2}

  • Because A and B are located in the same line x =5

=> the lenght of AB = \sqrt{(-2-2)^{2} } =\sqrt{-4^{2} } =4

  • Because A and B are located in the same line x =-5

=>  the lenght LM = \sqrt{(-6-6)^{2} } =\sqrt{-12^{2} } =12

  • Because ABC is similar to LMN

=> the ratio of LM : AB = 12:4 = 3:1

<=> the ratio LN : CA = 3:1

We need to find the lenght of CA

= \sqrt{(2-5)^2+(1-2)^2} = \sqrt{-3^{2} + -1^{2} } = \sqrt{10}

=> the lenght of LN = 3CA = 3\sqrt{10}

Let (x, y) is the coordinate of N, we have:

The length of LN: \sqrt{(x+5)^2+(y-6)^2} = 3\sqrt{10} = \sqrt{90}

Let try all the possible answer;

(3,4) => \sqrt{(3+5)^2+(4-6)^2} = \sqrt{8^{2} + -2^{2} } = \sqrt{90} True

So we choose (3,4)

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