Find the area of rectangle QRST , with vertices Q(−1,7) , R(5,7) , S(5,3) , and T(−1,3) .
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The formula to find the area of a rectangle given its vertices is to calculate the distance between two opposite vertices and then multiply those distances.
First, calculate the distance between Q and R:
Distance QR = √[(5 - (-1))^2 + (7 - 7)^2]
Distance QR = √[6^2 + 0]
Distance QR = √36
Distance QR = 6
Then, calculate the distance between S and T:
Distance ST = √[(-1 - 5)^2 + (3 - 3)^2]
Distance ST = √[(-6)^2 + 0]
Distance ST = √36
Distance ST = 6
Now, find the area of the rectangle by multiplying the distances:
Area = 6 * 6
Area = 36 square units
Therefore, the area of rectangle QRST is 36 square units.