Video Transcript
If π΄π΅πΆπ· is a parallelogram, where π΄ is the point eight, two and π΅ is the point
negative four, seven, find the slope of the line between π· and πΆ.
In this question, we are told that quadrilateral π΄π΅πΆπ· is a parallelogram, and
weβre given the coordinates of two of its vertices, π΄ and π΅. We need to use this to find the slope of the line between π· and πΆ. To find the slope of this line, we can start by sketching the parallelogram
π΄π΅πΆπ·. It is worth noting that we do not know the exact coordinates of πΆ and π·. So we cannot be sure of the exact dimensions of the shape.
We do need to make sure that we can transverse the vertices in the order π΄, π΅, πΆ,
π·. We obtain a sketch like the following. However, we will see that it is not necessary to know this information. We can recall that opposite sides in a parallelogram have the same length and are
parallel. In particular, we can note that this tells us that the line between π· and πΆ is
parallel to the line between π΄ and π΅. We can also recall that parallel lines have the same slope. So we can find the slope of the line between π· and πΆ by finding the slope of the
line between π΄ and π΅.
We can find the slope of the line between π΄ and π΅ by recalling the slope formula,
which tell us that the slope π of a line between two distinct points π₯ sub zero,
π¦ sub zero and π₯ sub one, π¦ sub one is given by π is equal to π¦ sub one minus
π¦ sub zero all over π₯ sub one minus π₯ sub zero. We can use the coordinates of points π΄ and π΅ and this formula to find the slope of
the line between π΄ and π΅, and hence the slope of the line between π· and πΆ.
We substitute the coordinates of these points into the slope formula to obtain π
equals seven minus two all over negative four minus eight. We can then evaluate this expression to get negative five over 12. We can then conclude that this must be the slope of the line between π· and πΆ since
it is parallel to the line between π΄ and π΅.