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Lydia graphed ΔLMN at the coordinates L (0, 0), M (2, 2), and N (2, −1). She thinks ΔLMN is a right triangle. Is Lydia's assertion correct? Yes; the slopes of segment LM and segment LN are opposite reciprocals. No; the slopes of segment LM and segment LN are not opposite reciprocals. Yes; the slopes of segment LM and segment LN are the same. No; the slopes of segment LM and segment LN are not the same.

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Answer:

No; the slopes of segment LM and segment LN are not opposite reciprocals

Step-by-step explanation:

slope of LM: (2 - 0)/(2 - 0)  = 1

slope of LN: (-1 - 0)/(2 - 0) = -1/2

Two lines are perpendicular when the multiplication of their slopes is equal to negative one, that is, they are opposite reciprocals. In this case:

slope of LM*slope of LN = 1*(-1/2) = -1/2

The correct option is

No; the slopes of segment LM and segment LN are not opposite reciprocals

  • The calculation is as follows:

slope of LM: [tex](2 - 0)\div (2 - 0)[/tex]  = 1

And,  

slope of LN: [tex](-1 - 0)\div (2 - 0)[/tex]= [tex]-1\div 2[/tex]

Here two lines should be perpendicular at the time  when the multiplication of their slopes is equalivalent to negative one.  

So,  

= slope of LM × slope of LN

[tex]= 1\times (-1\div 2)\\\\ = -1\div 2[/tex]

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