If A(−1, 3), B(4, 4), and C(8, 1), then classify ΔABC as scalene, isosceles, or equilateral? If there is not enough information to classify the triangle, then choose “The answer cannot be determined.” The answer cannot be determined. isosceles scalene eq

1 Answer
Mar 7, 2018

Scalene (since no two sides have the same length)

Explanation:

Given
#color(white)("XXX")A: color(green)(""(-1,3))#
#color(white)("XXX")B:color(magenta)(""(4,4))#
#color(white)("XXX")C:color(orange)(""(8,1))#

Using the Pythagorean Theorem
#color(white)("XXX")abs(AB)=sqrt((color(green)(-1)-color(magenta)4)^2+(color(green)3-color(magenta)4)^2)=sqrt(25+1)=sqrt(26)#

#color(white)("XXX")abs(AC)=sqrt((color(green)(-1)-color(orange)8)^2+(color(green)3-color(orange)1)^2)=sqrt(81+4)=sqrt(85)#

#color(white)("XXX")abs(BC)=sqrt((color(magenta)4-color(orange)8)^2+(color(magenta)4-color(orange)1)^2)=sqrt(16+9)=sqrt(25)#