Question

the approximate length of side xy is
the approximate length of side yz is
the approximate length of side zx is
the approximate perimeter of triangle xyz is

Explanation:

Answer:

(1) First, find the coordinates of the points. Let \(X(-3, - 1)\), \(Y(1,-4)\), \(Z(-5,-4)\)

• Use the distance - formula \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\)
• For side \(XY\):
• \(x_1=-3,y_1 = - 1,x_2 = 1,y_2=-4\)
• \(d_{XY}=\sqrt{(1+3)^2+(-4 + 1)^2}=\sqrt{16 + 9}=\sqrt{25}=5\)
• For side \(YZ\):
• \(x_1 = 1,y_1=-4,x_2=-5,y_2=-4\)
• \(d_{YZ}=\sqrt{(-5 - 1)^2+(-4 + 4)^2}=\sqrt{(-6)^2+0^2}=6\)
• For side \(ZX\):
• \(x_1=-5,y_1=-4,x_2=-3,y_2=-1\)
• \(d_{ZX}=\sqrt{(-3 + 5)^2+(-1 + 4)^2}=\sqrt{4 + 9}=\sqrt{13}\approx3.6\)
• The perimeter \(P=d_{XY}+d_{YZ}+d_{ZX}=5 + 6+3.6 = 14.6\)

(2) Answers:

• The approximate length of side \(XY\) is \(5\) units.
• The approximate length of side \(YZ\) is \(6\) units.
• The approximate length of side \(ZX\) is \(3.6\) units.
• The approximate perimeter of triangle \(XYZ\) is \(14.6\) units.