Answer:
Part a) The measure of the sides of triangle DEF are
[tex]d_D_E=\sqrt{90}\ units[/tex]
[tex]d_E_F=\sqrt{65}\ units[/tex]
[tex]d_D_F=\sqrt{221}\ units[/tex]
Part b) Is a scalene triangle
Step-by-step explanation:
we know that
the formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
we have the coordinates
D(8,-6) E(-1,-3) F(-2,5)
step 1
Find the length side DE
D(8,-6) E(-1,-3)
substitute in the formula
[tex]d=\sqrt{(-3+6)^{2}+(-1-8)^{2}}[/tex]
[tex]d=\sqrt{(3)^{2}+(9)^{2}}[/tex]
[tex]d_D_E=\sqrt{90}\ units[/tex]
step 2
Find the length side EF
E(-1,-3) F(-2,5)
substitute in the formula
[tex]d=\sqrt{(5+3)^{2}+(-2+1)^{2}}[/tex]
[tex]d=\sqrt{(8)^{2}+(-1)^{2}}[/tex]
[tex]d_E_F=\sqrt{65}\ units[/tex]
step 3
Find the length side DF
D(8,-6) F(-2,5)
substitute in the formula
[tex]d=\sqrt{(5+6)^{2}+(-2-8)^{2}}[/tex]
[tex]d=\sqrt{(11)^{2}+(-10)^{2}}[/tex]
[tex]d_D_F=\sqrt{221}\ units[/tex]
step 4
Classify the triangle by the measure of its sides
we have
[tex]d_D_E=\sqrt{90}\ units[/tex]
[tex]d_E_F=\sqrt{65}\ units[/tex]
[tex]d_D_F=\sqrt{221}\ units[/tex]
so
Is a scalene triangle, because is a triangle in which all three sides have different lengths.
