Question

Find the length of the longest side of the rectangle whose vertices are given. a(2, 1), b(5, 4), c(0, 3), d(3, 6)

Answer 1

First, you plot the coordinates to visualize the problem clearly. As you can see in the picture, the longest sides could either be one of those marked in red. This could be initially determined when you use visual estimation. We measure this using the distance formula: d = √[(x2-x1)^2 + (y2-y1)^2)]

Between coordinates (0,3) and (3,6)
d = √[(3-0)^2 + (6-3)^2)]
d= 4.24 units

Between coordinates (2,1) and (5,4)
d = √[(5-2)^2 + (4-1)^2)]
d= 4.24 units

They are of equal length. Both are the longest sides which measures 4.24 units.

Answer 2

Answer: 2√2

Step-by-step explanation:

These sides, when graphed, creates a rectangle. The rectangle has long sides that are parallel. We know the long side's points, so if we find the distance of the sides, (5, 4) and (3, 6), we get the equation:

AB^2 = (3 - 5)^2 + (6 - 4)^2

AB = √(3 - 5)^2 + (6 - 4)^2

AB = 2√2

I hope this helps, I just read the lesson and this is how you are supposed to do these equations.