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3 years ago

Through (2, 1) with slope of -3/2

Mathematics

1 answer:

DanielleElmas [232]3 years ago

8 0

Equation: Y= -3/2x + 4

Graph:

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One factor in flood safety along a levee is the area that will absorb water should the levee break. The coordinates that make up

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Let

$A(0,0)\\ B (2.8, 2.1)\\C(4.3, 4.4)$

using a graph tool

see the attached figure

The figure is a triangle

we know that

The Heron's Formula is a method for calculating the area of a triangle when you know the lengths of all three sides.

Hero's Formula is equal to

$Area=\sqrt{p*(p-a)*(p-b)*(p-c)}$

where

p is is half the perimeter of the triangle

a,b,c are the lengths of the sides of a triangle

Step $1$

Find the length sides of the triangle

a) Find the distance AB

$d =\sqrt{(y2-y1)^{2} +(x2-x1)^{2}}$

Substitute

$d =\sqrt{(2.1-0)^{2} +(2.8-0)^{2}}$

$d =3.5\ mi}$

b) Find the distance AC

$d =\sqrt{(y2-y1)^{2} +(x2-x1)^{2}}$

Substitute

$d =\sqrt{(4.4-0)^{2} +(4.3-0)^{2}}$

$d =6.15\ mi}$

c) Find the distance BC

$d =\sqrt{(y2-y1)^{2} +(x2-x1)^{2}}$

Substitute

$d =\sqrt{(4.4-2.1)^{2} +(4.3-2.8)^{2}}$

$d =2.75\ mi}$

Step $2$

Find the perimeter of the triangle

$Perimeter= 3.5+6.15+2.75 =12.4\ mi$

Find the half of the perimeter

$p=\frac{12.4}{2} = 6.2\ mi$

Step $3$

Find the area of the triangle

$Area=\sqrt{6.2*(6.2-3.5)*(6.2-6.15)*(6.2-2.75)}$

$Area=\sqrt{6.2*(2.7)*(0.05)*(3.45)}$

$Area= 1.69\ mi^{2}$

therefore

the answer is the option

a) 1.65 mi^2.

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