Question

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what is the perimeter of the triangle shown on the coordinate plane, to the nearest tenth of a unit?
20.6 units
22.7 units
25.6 units
27.6 units

Explanation:

Step1: Find the lengths of the sides using the distance formula

The distance formula is \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\).
Let the points be \(A(-5,4)\), \(B(1,4)\), \(C(3,-4)\).
For side \(AB\): \(x_1=-5,y_1 = 4,x_2=1,y_2 = 4\).
\(AB=\sqrt{(1-(-5))^2+(4 - 4)^2}=\sqrt{(6)^2+0^2}=6\).
For side \(BC\): \(x_1=1,y_1 = 4,x_2=3,y_2=-4\).
\(BC=\sqrt{(3 - 1)^2+(-4 - 4)^2}=\sqrt{2^2+(-8)^2}=\sqrt{4 + 64}=\sqrt{68}\approx8.2\).
For side \(AC\): \(x_1=-5,y_1 = 4,x_2=3,y_2=-4\).
\(AC=\sqrt{(3-(-5))^2+(-4 - 4)^2}=\sqrt{8^2+(-8)^2}=\sqrt{64+64}=\sqrt{128}\approx11.3\).

Step2: Calculate the perimeter

Perimeter \(P=AB + BC+AC\).
\(P=6+8.2 + 11.3=25.5\approx25.6\).

Answer:

25.6 units