What type of triangle is formed by joining the points D(7, 3), E(8, 1), and F(4,-1)?

1 Answer
Oct 1, 2016

A right-angled triangle is formed.

Explanation:

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1) calculate d the distance between the points of the triangles, use the distance formula :
#d=sqrt((x2−x1)^2+(y2−y1)^2#

#D(7,3), E(8,1),F(4,-1)#

#=> DE=sqrt((8-7)^2+(1-3)^2))=sqrt(1^2+2^2)=sqrt5#
#=> EF=sqrt((4-8)^2+(-1-1)^2)=sqrt(4^2+2^2)=sqrt20#
#=>DF==sqrt((4-7)^2+(-1-3)^2)=sqrt(3^2+4^2)=sqrt25=5#

Pythagorean theorem : #c^2=a^2+b^2#

The theorem states that: The sum of the squares of the lengths of the legs of a right triangle is equal to the square of the length of the hypotenuse.

Now we use the theorem to check and see if the triangle is right-angled or not :

#=> sqrt(25)^2=sqrt5^2+sqrt20^2#
#=> 25=5+20#

As #(DF)^2=(DE)^2+(EF)^2#, triangle #DEF# is right-angled.