Question

Triangle ABC has vertices at A(-2, 3), B(-3,-6), and C(2,-

1). Is triangle ABC a right triangle? If so, which angle is the
right angle?
w Ano
A(-2,3)
O No, the triangle has no right angles.
O Yes, the right angle is angle A.
O Yes, the right angle is angle B.
O Yes, the right angle is angle C.
6
5
4 -3 3-2 -1,5
2
6
x
3 4 5
C (2,-1)
B(-3,-6)

Answer 1

Yes, the right angle is angle B

Explanation:

we have

`A(-2, 3), B(-3,-6),C(2,-1)`

Plot the vertices

see the attached figure

we know that

If triangle ABC is a right triangle

then

Applying the Pythagoras Theorem

`AB^(2) =AC^(2)+BC^(2)`

the formula to calculate the distance between two points is equal to

`d=\sqrt{(y2-y1)^(2)+(x2-x1)^(2)}`

Find the distance AB

`A(-2, 3), B(-3,-6)`

substitute in the formula

`d=\sqrt{(-6-3)^(2)+(-3+2)^(2)}`

`d=\sqrt{(-9)^(2)+(-1)^(2)}`

`AB=√(82)\ units`

Find the distance BC

`B(-3,-6),C(2,-1)`

substitute in the formula

`d=\sqrt{(-1+6)^(2)+(2+3)^(2)}`

`d=\sqrt{(5)^(2)+(5)^(2)}`

`BC=√(50)\ units`

Find the distance AC

`A(-2, 3),C(2,-1)`

substitute in the formula

`d=\sqrt{(-1-3)^(2)+(2+2)^(2)}`

`d=\sqrt{(-4)^(2)+(4)^(2)}`

`AC=√(32)\ units`

Verify the Pythagoras theorem

`(√(82))^(2) =(√(32))^(2)+(√(50))^(2)`

`82=82` ---> is true

therefore

Is a right triangle and the right angle is B