(5,2),(3,-5),(-5,-1) find the area of triangle ?

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Answer 1 · 2018-04-24T06:17:27

#A = 32# Square Units

Let: #A(5,2)#, #B(3, -5)#, #C(-5, -1)#, then:

Shift #C# to Origin#(0, 0)#, and also:

Adjust #A# and #B# to compensate for the shift accordingly:

#C(-5+5 , -1+1) => C(0, 0)#
#A(5+5, 2+1) => A(10, 3)#
#B(3+5, -5+1) => C(8, -4)#

Then we can use the following:

Area of the triangle with vertices at:

#C(0, 0)#, #A(x_1, y_1)#, and #B(x_2, y_2)# is:

Area = #1/2|x_1 y_2 - x_2 y_1|#

Therefore in this case we get:

#A=1/2|(10)(-4)-(8)(3)|#

#A= 1/2|-40-24|#

#A=1/2|-64|#

#A= 1/2*64#

#A = 32# Square Units