What is the area of the rectangle?
(-3,1)
(3,4)
(1,1)
(7,2) a. 2√5 b. 3√5 c. 10√5 d. 30
To find the area of the rectangle, we need to find the length of the sides of the rectangle.
The length of the sides can be found using the distance formula:
Distance = √[(x2 - x1)^2 + (y2 - y1)^2]
The length of the rectangle with points (-3,1) and (3,4) is:
√[(3 - (-3))^2 + (4 - 1)^2]
= √[6^2 + 3^2]
= √[36 + 9]
= √45
= 3√5
The width of the rectangle with points (1,1) and (7,2) is:
√[(7 - 1)^2 + (2 - 1)^2]
= √[6^2 + 1^2]
= √[36 + 1]
= √37
To find the area of the rectangle, we multiply the length and width:
Area = (3√5)(√37)
= 3√(5*37)
= 3√185
Therefore, the area of the rectangle is approximately 13.6.
The closest answer choice is c. 10√5.