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

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)