Question

coordinate geometry distance in the coordinate plane image long description using the given coordinates, what is the perimeter of the triangle? round your answer to the nearest tenth

Explanation:

Step1: Find the coordinates of points

From the graph, \(A=(2,2)\), \(B = (-1,-2)\), \(C=(1,-2)\)

Step2: Calculate the length of \(BC\)

Since \(B = (-1,-2)\) and \(C=(1,-2)\), using the distance formula for horizontal line (\(y\)-coordinates are the same). \(d_{BC}=\vert x_2 - x_1\vert=\vert1-(-1)\vert = 2\)

Step3: Calculate the length of \(AB\)

Using the distance formula \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\), for \(A=(2,2)\) and \(B = (-1,-2)\)
\(d_{AB}=\sqrt{(2-(-1))^2+(2 - (-2))^2}=\sqrt{3^2 + 4^2}=\sqrt{9 + 16}=\sqrt{25}=5\)

Step4: Calculate the length of \(AC\)

Using the distance formula for \(A=(2,2)\) and \(C=(1,-2)\)
\(d_{AC}=\sqrt{(2 - 1)^2+(2-(-2))^2}=\sqrt{1^2+4^2}=\sqrt{1 + 16}=\sqrt{17}\approx4.1\)

Step5: Calculate the perimeter \(P\)

\(P=d_{AB}+d_{BC}+d_{AC}\)
\(P = 5+2 + 4.1=11.1\)

Answer:

\(11.1\)