Question

what is the perimeter of quadrilateral beat if it has vertices with coordinates, b(2, - 5), e(-3, - 3), a(1,5), and t(5,3)?
round your answer to the nearest whole number.
use the keypad to enter the answer in the box provided.
the perimeter of quadrilateral beat is units.

Explanation:

Step1: Use the distance formula

The distance formula between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\)
For \(BE\): \(x_1 = 2,y_1=-5,x_2=-3,y_2 = -3\)
\(BE=\sqrt{(-3 - 2)^2+(-3+5)^2}=\sqrt{(-5)^2+2^2}=\sqrt{25 + 4}=\sqrt{29}\approx5.39\)

Step2: Calculate \(EA\)

For \(EA\): \(x_1=-3,y_1=-3,x_2 = 1,y_2=5\)
\(EA=\sqrt{(1 + 3)^2+(5 + 3)^2}=\sqrt{4^2+8^2}=\sqrt{16+64}=\sqrt{80}\approx8.94\)

Step3: Calculate \(AT\)

For \(AT\): \(x_1 = 1,y_1=5,x_2=5,y_2=3\)
\(AT=\sqrt{(5 - 1)^2+(3 - 5)^2}=\sqrt{4^2+(-2)^2}=\sqrt{16 + 4}=\sqrt{20}\approx4.47\)

Step4: Calculate \(TB\)

For \(TB\): \(x_1=5,y_1=3,x_2=2,y_2=-5\)
\(TB=\sqrt{(2 - 5)^2+(-5 - 3)^2}=\sqrt{(-3)^2+(-8)^2}=\sqrt{9+64}=\sqrt{73}\approx8.54\)

Step5: Sum up the lengths

Perimeter \(P=BE + EA+AT+TB\)
\(P\approx5.39+8.94 + 4.47+8.54=27.34\approx27\)

Answer:

\(27\)