1. The points ( − 4, − 4), ( − 4, 4), (4, 4), and (4, − 4) form a square on a coordinate plane. How long is a side length of the square

Length of one side is 8 units

Step-by-step explanation:

Given

The centre of this square is positioned at the origin as visible form the four co-ordinates

All the four co-ordinates are such that they are 4 units along the x-axis and 4 units along the y-axis.

Let us take the following two co-ordinates - (4,4),(4,−4). The X value for these two co-ordinate points is 4 and the Y values are such that one point has y = 4 and the other has y = -4 i.e 8 units in between.  

Thus, length of one side is 8 units.  

there are lots of ways.   pick's theorem tells us if the vertices are lattice points the area a is

a = b/2 + i - 1

where b is the number of boundary lattice points and i is the number of interior lattice points.

in the figure i count b=16, i=50 so

a = 8 + 50 - 1 = 57

let's try the shoelace formula.   the area is half the sum of the cross products of the sides.  

a(-2,6)   -2(2)-6(-5) = 26

b(-5,2)   -5(-3) - 2(-2) = 19

c(-2,-3) -2(-3) - (-3)(4) = 18

d(4,-3)   4(3) - (-3)(5) = 27

e(5,3)   5(3) - 3(1) = 12

f(1,3)     1(6) - 3(-2) = 12

a(-2,6)

each of the cross products is twice the area of the triangle with the associated side and one vertex the origin. so the area of abo=26/2=13.

area = (1/2) (26 + 19 +   18 + 27 + 12 + 12) = 57

that checks!

15 batches are the most you can make

step-by-step explanation: