Respuesta :

TaeKwonDoIsDead

Answer:

"perpendicular"

Step-by-step explanation:

We need to find slope (m) of both line JK and LM

Slope has formula:

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Lets find slope of JK:

[tex]m=\frac{4-9}{7-1}\\m=-\frac{5}{6}[/tex]

Lets find slope of LM:

[tex]m=\frac{y_2-y_1}{x_2-x_1}\\m=\frac{1-13}{-2-8}\\m=\frac{6}{5}[/tex]

we know if we multiply two lines' slope and get -1, they are perpendicular. Let's check:

[tex]-\frac{5}{6}*\frac{6}{5}=-1[/tex]

Hence, they are perpendicular

akposevictor

The slope of JK is the negative reciprocal of the slope of LM, they are therefore perpendicular.

Note the following key-points regarding parallel lines and perpendicular lines:

  • The slope of two lines that are parallel to each other is the same.

  • If the slope of one line is 4, the slope of the other would be 4 if they are parallel lines.

  • The slope of perpendicular lines are always a negative reciprocal of each other.

  • If a line has slope value of 3/2, and the slope of another line is -2/3, both lines are perpendicular.

Let's find the slope of JK and LM to know if they are perpendicular, parallel or not:

  • Given:

[tex]j(1,9)\\\\k(7,4)\\\\l(8,13)\\\\m(-2,1)[/tex]

  • Find the slope of JK:

Slope formula = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

  • Let,

[tex]j(1,9) = (x_1, y_1)\\\\k(7,4) = (x_2, y_2)[/tex]

  • Plug in the values

[tex]\frac{4 - 9}{7-1} = \frac{-5}{6}[/tex]

The slope of JK is [tex]-\frac{5}{6}[/tex]

  • Find the slope LM:

Slope formula = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

  • Let,

[tex]L(8, 13) = (x_1, y_1)\\\\M(-2,1) = (x_2, y_2)[/tex]

  • Plug in the values

[tex]\frac{1-13}{-2 -8} = \frac{-12}{-10} = \frac{6}{5}[/tex]

  • The slope of LM is [tex]\frac{6}{5}[/tex]

The slope of JK, [tex]-\frac{5}{6}[/tex] is the negative reciprocal of the slope of LM, [tex]\frac{6}{5}[/tex], therefore, JK and LM are perpendicular.

Learn more here:

https://brainly.com/question/10703469

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