What is the area of a rectangle with vertices at (1, 7) , (5, 3) , (3, 1) , and (−1, 5) ?
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units²

Area =  16 units²

Step-by-step explanation:

Points to remember

Distance formula

The distance between two points (x1, y1) and (x2, y2) is given by

Distance = √[(x2 - x1)² + (y2 - y1)²]

To find the length and breadth of rectangle

Let the points be  (1, 7) , (5, 3)

Distance = √[(x2 - x1)² + (y2 - y1)²]

 = √[(5 - 1)² + (3 - 7)²]

 =  √[(4)² + (-4)²]

 = √32 = 4√2

If the points be  (5, 3) , (3, 1)

Distance = √[(x2 - x1)² + (y2 - y1)²]

 = √[(3 - 5)² + (1 - 3)²]

 =  √[(-2)² + (-2)²]

 = √8 = 2√2

Length = 4√2 and breadth = 2√2

To find the area of rectangle

Area = Length * Breadth

 = 4√2 * 2√2

 = 16 units²

16 units

Step-by-step explanation:

i have answered ur question

answer: the first graph

step-by-step explanation: