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.]

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)