### Video Transcript

Given that the coordinates of the
points π΄, π΅, πΆ, and π· are negative 15, eight; negative six, 10; negative eight,
negative seven; and negative six, negative 16, respectively, determine whether line
π΄π΅ and line πΆπ· are parallel, perpendicular, or neither.

Points π΄ and π΅ fall on the line
π΄π΅ and points πΆ and π· fall on the line πΆπ·. To classify the lines, we have to
remember: parallel lines have the same slope and they do not intersect. Perpendicular lines have negative
reciprocal slopes and intersect at a 90-degree angle. And neither are lines that are not
parallel or perpendicular, lines that do intersect but do not form a right
angle. This means to consider whether or
not these lines are parallel or perpendicular, we need to know the slopes of these
lines.

In the general form, π¦ equals ππ₯
plus π, the π represents the slope. And we can find the slope π if we
have two points by saying π equals π¦ two minus π¦ one over π₯ two minus π₯
one. In order to categorize these lines,
we need to find the slopes of line π΄π΅ and line πΆπ·. We can start with line π΄π΅. Let point π΄ be π₯ one, π¦ one and
point π΅ be π₯ two, π¦ two. Then, the slope will be 10 minus
eight over negative six minus negative 15. 10 minus eight is two. Negative six minus negative 15 is
negative six plus 15, which is positive nine. So, we can say that the slope of
line π΄π΅ is two-ninths.

We repeat this process for line
πΆπ·. Let πΆ be π₯ one, π¦ one and π· be
π₯ two, π¦ two. And weβll get π equals negative 16
minus negative seven over negative six minus negative eight. Negative 16 minus negative seven is
negative 16 plus seven, which is negative nine. Negative six minus negative eight
is negative six plus eight which is two. The slope of line πΆπ· is then
negative nine over two.

If we compared these two slopes,
negative nine over two is the negative reciprocal of two over nine. And if you werenβt sure, you can
multiply them together. Reciprocals multiply together to
equal one and negative reciprocals multiply together to equal negative one. These two slopes are the negative
reciprocals of one another, making these lines perpendicular.