What is the perimeter of the vertices (1,1)(7,1)(1,9)

Question

It’s the perimeter of the square

Answer 1

If you plot the three points on a graph and draw straight lines between them, you will see you have a right triangle, which is half of the full rectangle. But you really only need to know the length and width based on the equation for the perimeter for a rectangle, P = 2(L + W). After plotting the three points, you will see your length parallel to the x-axis is 6 units, and your width parallel to the y-axis is 8 units. Based on the area of a rectangle, P = 2(L + W) = 2(6 + 8) = 2(14) = 28 units. (Note: If you want to see the full rectangle on the graph, you can place the fourth point at (7,9))

If you don't have paper, you can look at the three sets of coordinates and see point (1,1) has a shared coordinate with the other two points (i.e., (1,1) has the same x-coordinate as point (1,9), and the same y-coordinate as (7,1)). Visually, this make (1,1) the corner point relative to the other two points at a right angle. From here, you can calculate the distance from this corner to the other points based on the difference between the coordinate that is not shared. See below:

Comparing (1,1) to (7,1): The second point is 6 units over from (1,1) along the x-axis (7 minus 1).

Comparing (1,1) to (1,9): The second point is 8 units up from (1,1) along the y-axis (9 minus 1).

Again using the equation for the perimeter of a rectangle, P = 2(Length + Width) = 2(6 + 8) = 2(14) = 28 units.