Video Transcript
Rectangle ๐ด๐ต๐ถ๐ท is graphed in the coordinate plane with its vertices at ๐ด zero, zero; ๐ต negative seven, zero; ๐ถ negative seven, negative four; and ๐ท zero, negative four. Find its perimeter.
So here weโre given four vertices with their coordinate references. Weโre told that these four points will create a rectangle. Letโs begin by getting some grid paper and drawing these four points. So here we have ๐ด at the coordinate zero, zero; ๐ต at negative seven, zero; ๐ถ at negative seven, negative four; and ๐ท at zero, negative four. Joining these four vertices together would indeed give us a rectangle. We know this to be true as a rectangle is defined as a quadrilateral with four right angles.
So now that weโve drawn ๐ด๐ต๐ถ๐ท, letโs see if we can calculate its perimeter. And we should remember that the perimeter is the distance around the outside edge of a shape. In order to find the perimeter of this rectangle, weโll need to know the length of all of the sides. So letโs begin with this length of ๐ด๐ต. We could find this length either by counting the squares on the grid or by noticing that the line goes from zero on the ๐ฅ-axis to negative seven on the ๐ฅ-axis. Therefore, the length of this line would be seven units long. As this is a rectangle, we know that one of the properties is that opposite sides are congruent. So this means that the length ๐ถ๐ท would also be seven units.
The line from ๐ต to ๐ถ goes from zero on the ๐ฆ-axis to negative four on the ๐ฆ-axis, so we know that this will be four units long. Therefore, ๐ด๐ท will also be the same at four units long. To find the perimeter then, we add these four lengths together. So we have seven plus four plus seven plus four, which gives us 22. We werenโt given any units in the question as itโs a coordinate grid, so weโd have 22 length units for the value of the perimeter.
