Rectangle 𝐴𝐵𝐶𝐷 is graphed in the coordinate plane with its vertices at 𝐴 zero, zero; 𝐵 negative seven, zero; 𝐶 negative seven, negative four; and 𝐷 zero, negative four. Find its perimeter.
So here we’re given four vertices with their coordinate references. We’re told that these four points will create a rectangle. Let’s begin by getting some grid paper and drawing these four points. So here we have 𝐴 at the coordinate zero, zero; 𝐵 at negative seven, zero; 𝐶 at negative seven, negative four; and 𝐷 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 we’ve drawn 𝐴𝐵𝐶𝐷, let’s 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, we’ll need to know the length of all of the sides. So let’s begin with this length of 𝐴𝐵. We could find this length either by counting the squares on the grid or by noticing that the line goes from zero on the 𝑥-axis to negative seven on the 𝑥-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 𝐶𝐷 would also be seven units.
The line from 𝐵 to 𝐶 goes from zero on the 𝑦-axis to negative four on the 𝑦-axis, so we know that this will be four units long. Therefore, 𝐴𝐷 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 weren’t given any units in the question as it’s a coordinate grid, so we’d have 22 length units for the value of the perimeter.