Question

​​ What is the area of a rectangle with vertices at ​ (−4, 0) ​, ​ (−3, 1) ​ , (0, −2) , and (−1, −3) ? Enter your answer in the box. Do not round any side lengths. units

Answer 1

What we know:
Area=l x w
vertices at (-4,0),(-3,1), (0,-2),(-1,-3)
pythagorean formula=a²+b²=h²

What we need to find:
Area
 
Finding length:
Length of rectangle is from point (-4,0) to (-1,-3), found it by plotting the points on graph paper. Went down 3 units and right 3 units to go from one point to the other, these are the a and b in the pythagorean formula.

a²+b²=h²
(3)²=(3)²=h²
9+9=h²
18=h²
√18=√h²
√18=h

Finding width:
Width of rectangle is from point (-4,0) to (-3,1), found it by plotting the points on graph paper. Went up 1 unit and right 1 unit to go from one point to the other, these are the a and b in the pythagorean formula.

a²+b²=h²
(1)²+(1)²=h²
1+1=h²
2=h²
√2=√h²
√2=h

Now we can find area,
Area= l x w
        = √18 x√2
        =√36=6
Area=6

Remember that when we square root a number we get two solutions, one negative and one positive but since length, width and area are positive we only use positive solutions.