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# can anyone help

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A triangle has coordinates A(1,1),B(4,2),C(3,5).  What is the area of triangle ABC?

Sep 5, 2020

#3
+1440
+6

A triangle has coordinates A(1,1),B(4,2),C(3,5).  What is the area of triangle ABC?

AB = BC = sqrt( 10)

Angle ABC = 90 degrees

area = (AB * BC) / 2 = 5

Sep 5, 2020

#1
+10829
+2

A triangle has coordinates A(1,1),B(4,2),C(3,5). What is the area of triangle ABC?

Hello Guest!

$$y=m(x-x_1)+y_1$$

$$m_a=\frac{5-2}{3-4}=-3\\ m_b=\frac{5-1}{3-1}=2\\ m_c=\frac{2-1}{4-1}=\frac{1}{3}$$

$$y_a=-3(x-4)+2=-3x+14\\ y_b=2(x-1)+1=2x-1\\ y_c=\frac{1}{3}(x-1)+1=\frac{1}{3}x+\frac{2}{3}$$

$$A_{ABC}=\int _3^4(-3x+14)+\int_1^3(2x-1)-\int_1^4(\frac{1}{3}x+\frac{2}{3})$$

$$A_{ABC}=|-\frac{3}{2}x^2+14x|_3^4+|x^2-x|_1^3-|\frac{1}{6}x^2+\frac{2}{3}x|_1^4$$

$$A_{ABC}=(-24+56+13.5-42)+(9-3-1+1)$$

$$-(\frac{16}{6}+\frac{8}{3}-\frac{1}{6}-\frac{2}{3})=5$$

$$\large A_{ABC}=5$$
!

Sep 5, 2020
edited by asinus  Sep 5, 2020
edited by asinus  Sep 5, 2020
edited by asinus  Sep 5, 2020
#2
+861
+3

A triangle has coordinates A(1,1),B(4,2),C(3,5).  What is the area of triangle ABC?

Area = {sqrt[10 - (√20/2)]} * √20 / 2 = 5 u2

Sep 5, 2020
edited by jugoslav  Sep 5, 2020
edited by jugoslav  Sep 5, 2020
edited by jugoslav  Sep 5, 2020
edited by jugoslav  Sep 5, 2020
edited by jugoslav  Sep 5, 2020
#3
+1440
+6

A triangle has coordinates A(1,1),B(4,2),C(3,5).  What is the area of triangle ABC?

AB = BC = sqrt( 10)

Angle ABC = 90 degrees

area = (AB * BC) / 2 = 5

Dragan Sep 5, 2020