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If line segment BC is considered the base of triangle ABC, what is the corresponding height of the triangle?

0.625 units
0.8 units
1.25 units
1.6 units

If line segment BC is considered the base of triangle ABC what is the corresponding height of the triangle 0625 units 08 units 125 units 16 units class=

Respuesta :

Answer:

1.6 units

Step-by-step explanation:

Coordinates of A : (-1,1)

Coordinates of B : (3,2)

Coordinates of C :( -1,-1)

Now to find the length of the sides of the triangle we will use distance formula :

[tex]d =\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

To find length of AB

A = [tex](x_1,y_1)=(-1,1)[/tex]

B= [tex](x_2,y_2)=(3,2)[/tex]

Now substitute the values in the formula:

[tex]d =\sqrt{(3-(-1))^2+(2-1)^2}[/tex]

[tex]d =\sqrt{(4)^2+(1)^2}[/tex]

[tex]d =\sqrt{16+1}[/tex]

[tex]d =\sqrt{17}[/tex]

[tex]d =4.12[/tex]

Now to find length of BC

B= [tex](x_1,y_1)=(3,2)[/tex]

C = [tex](x_2,y_2)=(-1,-1)[/tex]

Now substitute the values in the formula:

[tex]d =\sqrt{(-1-3)^2+(-1-2)^2}[/tex]

[tex]d =\sqrt{(-4)^2+(-3)^2}[/tex]

[tex]d =\sqrt{16+9}[/tex]

[tex]d =\sqrt{25}[/tex]

[tex]d =5[/tex]

Now to find length of AC

A = [tex](x_1,y_1)=(-1,1)[/tex]

C = [tex](x_2,y_2)=(-1,-1)[/tex]

Now substitute the values in the formula:

[tex]d =\sqrt{(-1-(-1))^2+(-1-1)^2}[/tex]

[tex]d =\sqrt{(0)^2+(-2)^2}[/tex]

[tex]d =\sqrt{4}[/tex]

[tex]d =2[/tex]

Thus the sides of triangle are of length 4.12, 5 and 2

Now to find area of triangle we will use heron's formula :

To calculate the area of given triangle we will use the heron's formula :

[tex]Area = \sqrt{s(s-a)(s-b)(s-c)}[/tex]

Where [tex]s = \frac{a+b+c}{2}[/tex]

a,b,c are the side lengths of triangle  

a = 4.12

b=5

c=2

Substitute the values

Now substitute the values :

[tex]s = \frac{4.12+5+2}{2}[/tex]

[tex]s =5.56[/tex]

[tex]Area = \sqrt{5.56(5.56-4.12)(5.56-5)(5.56-2)}[/tex]

[tex]Area = 3.99[/tex]

Now to find the height of altitude corresponding to side BC

So, formula of area of triangle [tex]=\frac{1}{2} \times Base \times Height[/tex]

Since Area = 3.99 square units

So,[tex]3.99 =\frac{1}{2} \times BC \times Height[/tex]

So,[tex]3.99 =\frac{1}{2} \times 5\times Height[/tex]

[tex]3.99 =2.5 \times Height[/tex]

[tex]\frac{3.99}{2.5}=Height[/tex]

[tex]1.596=Height[/tex]

Thus the altitude corresponding to the BC is of length 1.596 unit  ≈ 1.6 units

Thus Option D is correct.

onyebuchinnaji

The corresponding height of the triangle with line segment BC as its base is determined as 1.6 units.

Length AB of the triangle

The length AB of the triangle is calculated from the following coordinate points;

(x₁, y₁) = (-1, 1)

(x₂, y₂) = (3, 2)

[tex]|AB| = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2} \\\\|AB| = \sqrt{(3+1)^2 + (2-1)^2} \\\\|AB| = 4.12 \ units[/tex]

Length BC of the triangle

The length BC of the triangle is calculated from the following coordinate points;

(x₁, y₁) = (3, 2)

(x₂, y₂) = (-1, -1)

[tex]|BC| = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2} \\\\|BC| = \sqrt{(3+1)^2 + (2+1)^2} \\\\|BC| = 5 \ units[/tex]

Length AC of the triangle

The length AC of the triangle is calculated from the following coordinate points;

(x₁, y₁) = (-1, 1)

(x₂, y₂) = (-1, -1)

[tex]|AC| = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2} \\\\|AC| = \sqrt{(0)^2 + (-2)^2} \\\\|AC| = 2 \ units[/tex]

Area of the triangle

The area of the triangle is determined by applying Heron's formula as follows;

[tex]A = \sqrt{s(s- a)(s -b)(s-c)} \\\\s = \frac{a+b+c}{2} = \frac{4.12 + 5 + 2}{2} = 5.56\\\\A = \sqrt{5.56(5.56- 4.12)(5.56 -5)(5.56 - 2)}\\\\A = 4.0 \ units^2[/tex]

Height of the triangle

The height of the triangle is calculated as follows;

[tex]A = \frac{1}{2} bh\\\\h = \frac{2A}{b} \\\\h = \frac{2 \times 4}{5} \\\\h = 1.6 \ units[/tex]

Thus, the corresponding height of the triangle with line segment BC as its base is determined as 1.6 units.

Learn more about area of triangle here: https://brainly.com/question/21735282

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