find the length of a side of the square with vertices at (5,4), (1,5), (0,1), and (4,0) then find the area of the square?

Question

i need help on homework due tomorrow

Answer 1

All sides of a square are equal, so pick any two consecutive vertices and use the distance formula to find the distance between them. That distance is the length of all sides of the square.

 

Once you have that length, use a formula for the area of a square such as A = s² where A is area and s is the length of a side

Answer 2

If you plot this on the Cartesian coordinate plane

you see that your pairs of parallel sides making

your square are  (0,1) to (4,0) parallel to (1,5) to (5,4)

for width... and (0,1) to (1,5) parallel to (4,0) to (5,4)

for length.

 

Find the length of a side from the distance formula:

d = √[(x₂-x₁)²+(y₂-y₁)²]

 

Pick one side... Let's use (0,1) to (4,0)

d = √[(4-0)²+(0-1)²] = √(16+1) = √17

 

You side lengths are √17 units

 

The area is s² = (√17)² = 17 square units