# Question Video: Finding the Area of a Parallelogram Using the Distance Formula Mathematics

Where must the coordinates of point πΆ be so that π΄π΅πΆπ· is a parallelogram? In that case, what is the area of the parallelogram?

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### Video Transcript

Where must the coordinates of points πΆ be so that π΄π΅πΆπ· is a parallelogram? In that case, what is the area of the parallelogram?

In this question, weβre asked to make a parallelogram. We can remember that a parallelogram has two pairs of parallel and congruent sides. So if we look at our length π΄π΅, we can see that it must be five units long. Therefore, to draw a line from π· to πΆ, this must also be a horizontal line of length five units. We can confirm the coordinates of point πΆ by checking that the line π΅πΆ is parallel to the line π΄π·. We can see that on π΄π·, we moved three squares horizontally and seven squares vertically.

And to go from π΅ to πΆ, we can see that itβs also three squares horizontally and seven squares vertically. So line π΅πΆ is horizontal to π΄π· and confirms our point πΆ is that the coordinate six, five. Itβs worth noting at this point that our coordinate at negative four, five would also have created a parallelogram. However, we were told that our parallelogram was called π΄π΅πΆπ·. And in order to obey naming conventions, we list the vertices of a shape in the order of travel. If πΆ was to the left of π·, then the shape would have been called π΄π΅π·πΆ, which is not what we were told. And therefore, πΆ is not at negative four, five.

And now, for the second part of the question, using our πΆ coordinate, weβre asked for the area of the parallelogram. We can find the area of a parallelogram by multiplying the base times the vertical or perpendicular height. So using our formula then of base times height, we have our base of five units and a height of seven. So five times seven is 35.

So our final answer then is point πΆ is at coordinate six, five and the area is 35.