Question

9 look at triangle def.
what are the lengths, to the nearest hundredth,
of the sides of triangle def?
write your answers in the spaces provided.
de = units
ef = units
fd = units

Explanation:

Step1: Find coordinates

Assume each grid is 1 unit. Coordinates: \(D(-1,2)\), \(E(4,-4)\), \(F(-9,-4)\)

Step2: Use distance formula \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\)

For \(DE\):
\(x_1=-1,y_1 = 2,x_2 = 4,y_2=-4\)
\(DE=\sqrt{(4 - (-1))^2+(-4 - 2)^2}=\sqrt{5^2+(-6)^2}=\sqrt{25 + 36}=\sqrt{61}\approx7.81\)
For \(EF\):
\(x_1 = 4,y_1=-4,x_2=-9,y_2=-4\)
\(EF=\sqrt{(-9 - 4)^2+(-4-(-4))^2}=\sqrt{(-13)^2+0^2}=13.00\)
For \(FD\):
\(x_1=-9,y_1=-4,x_2=-1,y_2 = 2\)
\(FD=\sqrt{(-1-(-9))^2+(2-(-4))^2}=\sqrt{8^2+6^2}=\sqrt{64 + 36}=\sqrt{100}=10.00\)

Answer:

\(DE = 7.81\) units, \(EF = 13.00\) units, \(FD = 10.00\) units