Question

REALLY IMPORTANT

triangle ABC is similar to LMN, which is formed using LM, as shown

What could be the coordinates of point N?
(3,4)
(4,-3)
(-3,4)
(4,3)

Answer 1

a

Explanation:

Answer 2

we choose (3,4)

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:

`√((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

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

=> the lenght of LN = 3CA = 3
`√(10)`

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

The length of LN:
`√((x+5)^2+(y-6)^2) = 3√(10)` =
`√(90)`

Let try all the possible answer;

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

So we choose (3,4)