How do I find the perimeter of the triangle with the vertices (-2,2), (0,4), (1,-4)?

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Answer 1 · 2018-06-13T18:20:22

#color(blue)(17.60 " 2 d.p.")#

The perimeter is the sum of all the lengths of the sides of the triangle.

Let #A=(-2,2), B=(0,4), C=1,-4)#

So we have sides:

#AB, BC, AC#

We can find the lengths of each side using the distance formula:

#|d|=sqrt((x_2-x_1)^2+(y_2-y_1)^2)#

For #AB#

#|AB|=sqrt((0-(-2))^2+(4-2)^2)=sqrt(8)=2sqrt(2)#

For #BC#

#|BC|=sqrt((1-0)^2+(-4-4)^2)=sqrt(65)#

For #AC#

#|AC|=sqrt((1-(-2))^2+(-4-2)^2)=sqrt(45)=3sqrt(5)#

#"Perimeter"=AB+BC+AC=2sqrt(2)+sqrt(65)+3sqrt(5)~~17.59888880#

#color(blue)(17.60 " 2 d.p.")#