Given A(-3, -6), B(3,2), C(7,-1), how do you prove that ABC is a right triangle and not isosceles?

2 Answers
Jan 17, 2018

First of all you need to find the length of the three sides AB,BC,AC.

Explanation:

You can find the length of the sides using distance formula.
After calculating the length of the sides check if length of any two sides is equal or not.If it is equal, the triangle is isosceles otherwise not.
Same way you can check if the triangle is right angles or not.
Put the values of the sides in Pythagoras theorem [#H^2 = P^2 + B^2#].If the square of the largest side is equal to sum of squares of other two sides,the triangle is right-angled.
Now you can check whether the triangle is isosceles or right-angled.

Jan 17, 2018

#CA^2 = AB^2 +BC^2# , so it is right triangle and since
# AB != BC != CA#, and hence it is not isosceles triangle.

Explanation:

#A(-3,-6),B(3,2),C(7,-1) #

Distance between two points #(x_1,y_1) and (x_2,y_2)# is

#D= sqrt((x_1-x_2)^2+(y_1-y_2)^2)#or

Length of #AB# is #AB^2=(-3-3)^2+(-6-2)^2) =100# unit

Length of #BC# is #BC^2=(3-7)^2+(2+1)^2) =25# unit

Length of #CA# is #CA^2=(7+3)^2+(-1+6)^2) =125# unit

From above length of sides of triangle it is observed that

#CA^2 = AB^2 +BC^2 ; (125=100+25)# ,which is property

of a right triangle. #CA# is hypotenuse , #AB and BC# are

perpendicular sides. # AB != BC != CA#. Since no two sides

are equal in length, the triangle is not isosceles. [Ans]