Video: Finding the Area of a Parallelogram Using the Distance Formula

Where must the coordinates of point 𝐢 be so that 𝐴𝐡𝐢𝐷 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 𝐢 be so that 𝐴𝐡𝐢𝐷 is a parallelogram? In that case, what is the area of the parallelogram?

In this question, we’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 𝐴𝐡, we can see that it must be five units long. Therefore, to draw a line from 𝐷 to 𝐢, this must also be a horizontal line of length five units. We can confirm the coordinates of point 𝐢 by checking that the line 𝐡𝐢 is parallel to the line 𝐴𝐷. We can see that on 𝐴𝐷, we moved three squares horizontally and seven squares vertically.

And to go from 𝐡 to 𝐢, we can see that it’s also three squares horizontally and seven squares vertically. So line 𝐡𝐢 is horizontal to 𝐴𝐷 and confirms our point 𝐢 is that the coordinate six, five. It’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 𝐴𝐡𝐢𝐷. And in order to obey naming conventions, we list the vertices of a shape in the order of travel. If 𝐢 was to the left of 𝐷, then the shape would have been called 𝐴𝐡𝐷𝐢, which is not what we were told. And therefore, 𝐢 is not at negative four, five.

And now, for the second part of the question, using our 𝐢 coordinate, we’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 𝐢 is at coordinate six, five and the area is 35.

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