Question

Triangle ABC has vertices with Alx, 3).
B(-3,-1), and C(-1,-4). Determine
and state a value of x that would make
triangle ABC a right triangle. Justify why
AABC is a right triangle. [The use of the
set of axes below is optional.]

Answer 1

Answer:

x = 3

This triangle ABC will be a right triangle as its sides obey the Pythagoras theorem.

Step-by-step explanation:

Let us assume that the triangle Δ ABC has vertices A(x,3), B(-3,-1) and C(-1,-4) and it is a right triangle.  

We have to determine x.

Applying the Pythagoras Theorem,

AB² + BC² = AC² {If AC is the hypotenuse of the right triangle}

⇒ [(x + 3)² + 4²] + [(- 2)² + 3²} = (x + 1)² + 7²

⇒ x² + 6x + 38 = x² + 2x + 50

⇒ 4x = 12

⇒ x = 3 (Answer)

This triangle ABC will be a right triangle as its sides obey the Pythagoras theorem. (Answer)