Video Transcript
If 𝐴𝐵𝐶𝐷 is a parallelogram, where 𝐴 is the point eight, two and 𝐵 is the point
negative four, seven, find the slope of the line between 𝐷 and 𝐶.
In this question, we are told that quadrilateral 𝐴𝐵𝐶𝐷 is a parallelogram, and
we’re given the coordinates of two of its vertices, 𝐴 and 𝐵. We need to use this to find the slope of the line between 𝐷 and 𝐶. To find the slope of this line, we can start by sketching the parallelogram
𝐴𝐵𝐶𝐷. It is worth noting that we do not know the exact coordinates of 𝐶 and 𝐷. 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 𝐴, 𝐵, 𝐶,
𝐷. 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 𝐷 and 𝐶 is
parallel to the line between 𝐴 and 𝐵. We can also recall that parallel lines have the same slope. So we can find the slope of the line between 𝐷 and 𝐶 by finding the slope of the
line between 𝐴 and 𝐵.
We can find the slope of the line between 𝐴 and 𝐵 by recalling the slope formula,
which tell us that the slope 𝑚 of a line between two distinct points 𝑥 sub zero,
𝑦 sub zero and 𝑥 sub one, 𝑦 sub one is given by 𝑚 is equal to 𝑦 sub one minus
𝑦 sub zero all over 𝑥 sub one minus 𝑥 sub zero. We can use the coordinates of points 𝐴 and 𝐵 and this formula to find the slope of
the line between 𝐴 and 𝐵, and hence the slope of the line between 𝐷 and 𝐶.
We substitute the coordinates of these points into the slope formula to obtain 𝑚
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 𝐷 and 𝐶 since
it is parallel to the line between 𝐴 and 𝐵.
