Respuesta :
Answer:
The area of the triangle is 7.5 unit²
Step-by-step explanation:
Here we have the coordinates given as
(-3, 5) (-3, 8) and (2, 5)
Let us call the points A = (-3, 5)
B = (-3, 8) and
C = (2, 5)
Therefore the lengths of the sides of the triangle are
AB = a = [tex]\sqrt{(-3-(-3))^2+(5-8)^2} = 3[/tex]
AC = b = [tex]\sqrt{(-3-2)^2+(5-5)^2} = 5[/tex]
BC = c = [tex]\sqrt{(-3-2)^2+(8-5)^2} = \sqrt{34}[/tex]
Therefore the Area can be derived from Heron's formula which is
A = [tex]\sqrt{s\times (s-a)\times (s-b)\times (s-c)}[/tex] where s = semi perimeter or (a + b + c)/2
Therefore, plugging the values, we get
s = (3 + 5 + √34)/2 = 6.9155≈6.92
A = [tex]\sqrt{6.92\times (6.92-3)\times (6.92-5)\times (6.92-\sqrt{34} )}[/tex] = 7.499≈7.5.
Answer:
67.5 square units
Step-by-step explanation:
The points (-3, 5) and ( -3, 8) form a vertical segment, and the points (-3, 5) and ( 2, 5) form a horizontal segment, so the triangle has a right angle.
The base of the triangle is the segment formed by the points (-3, 5) and ( 2, 5), and their distance is:
D1 = sqrt((-3-2)^2 + (5-5)^2) = 5
The height of the triangle is the segment formed by the points (-3, 5) and ( -3, 8), and their distance is:
D2 = sqrt((-3+3)^2 + (5-8)^2) = 3
If the triangle is dilated by a scale of 3, so the base is D1*3 = 15 and the height is D2*3 = 9, then the area is:
The area of a triangle is Base * Height / 2, so we have that:
Area = 15 * 9 / 2 = 67.5 square units
