Question

Triangle ABC has vertices A(-4,4), B(6,0), C(-4,0). Is triangle ABC a right triangle?

Answer 1

YES

Answer 2

https://www.desmos.com/calculator/xcbodd3cq6

u can draw the lines

Answer 3

first we find the length of all the AB BC AC;
\[ds = \sqrt{((x1-x2)^2 +(y1-y2)^2)}\]

Answer 4

the length of AB if we take A(-4,4) B(6,0) :-
ds = sqrt(6+4)^2 + (0-4)^2) = sqrt(116)

Answer 5

the length of BC , B(6,0) C(-4,0)
ds = sqrt((6+4)^2 -0) = 10

Answer 6

the length of AC , C(-4,0) A(-4,4);
ds =sqrt(( -4 - -4)^2 + (4-0)^2) = 4;

Answer 7

you have AB = sqrt(116) AC = 4 and BC = 10;
to proof that this triangle you need to proof that every two of edges bigger than the third

Answer 8

AB + BC > AC sqrt(116) +10 > 4t his correct;
BC + AC > AB 10 + 4 > sqrt(116); this correct
AC + AB > sqrt(116) + 4 > 10 this correct

we prrof that this traingle

Answer 9

the second Question :- are this triangle is "Right triangle" ?

Answer 10

if the traingle pythagorean theorem then the traingel is Right traingle

Answer 11

\[(AB)^2 = (BC)^2 + (AC)^2\]

116 = 16 + 100 // then it's correct this is Right triangle