Answer:
The answer is below
Step-by-step explanation:
The distance between two points A(x₁, y₁) and B(x₂, y₂) on the coordinate is:
[tex]Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\\\[/tex]
An equilateral triangle is a triangle with three equal sides (all sides are equal).
a) Given vertices at A(-2,2), B(1,5), and C(-3,6):
[tex]AC=\sqrt{(-3-(-2))^2+(6-2)^2}=\sqrt{1+16}=\sqrt{17}=4.12\ unit\\\\AB=BC=AC=4.12\ unit[/tex]
b) Perimeter = AB + BC + AC = 3 * AC = 3 * 4.12 = 12.36 unit
c) If the scale factor is increased by 4, all the sides would also increase by 4. Hence the new length would be:
A'B' = B'C' = A'C' = 4 * AC = 4 * 4.12 = 16.48 unit
d) Perimeter = A'B' + B'C' + A'C' = 3 * A'C' = 3 * 16.48 = 49.44 unit
e) Area = [tex]\frac{\sqrt{3} }{4}*AC^2=\frac{\sqrt{3} }{4} *4.12^2=7.35\ unit^2[/tex]
