Question

Determine if JK and LM parallel, perpendicular, or neither .

Answer 1

3 - Perpendicular.

4 - Parallel.

Explanation:

`(y_(2)-y_(1) )/(x_(2)-x_(1) )`

`JK = (1-(-7))/(-4-(-10)) = (8)/(6) = (4)/(3)`

`LM = (-2-2)/(-6-(-3)) = (-4)/(3)`

Perpendicular, because two lines are considered perpendicular if their slopes are opposite reciprocals.

`JK = (-2-(-2))/(3-11) = (0)/(-8) = 0`

`LM = (-2-(-7))/(1-1) = (5)/(0) = 0`

Answer 2

JK and LM are parallel.

JK and LM are neither parallel nor perpendicular.

JK and LM are neither parallel nor perpendicular.

To determine whether two lines are parallel, perpendicular, or neither, we can examine the slopes of the lines.

For two lines to be parallel, their slopes must be equal. For two lines to be perpendicular, the product of their slopes must be -1.

Let's calculate the slopes for the given line segments:

Line Segment JK:

slope of JK = -1

Line Segment LM:

slope of LM = -1

The slopes of JK and LM are equal, so they are parallel.

Line Segment JK:

slope of JK = 4/3

Line Segment LM:

slope of LM = 0

The product of the slopes (slope of JK × slope of LM) is 0, which is not equal to -1. Therefore, JK and LM are neither parallel nor perpendicular.

Line Segment JK:

slope of JK = 0

Line Segment LM:

slopes of LM = 5/-3

Therefore, JK and LM are neither parallel nor perpendicular.