Question

(-2, 1) (-2, 5) and(5, 5) determine whether the given points are vertices of right triangle​

Answer 1

Answer:

To prove:

A(2,−2),B(−2,1) and C(5,2) are the vertices of a right angled-triangle.

Proof:

By distance formula,

AB=

(−2−2)

2

+(1+2)

2

=

16+9

=

25

=5

BC=

(−2−5)

2

+(1−2)

2

=

(−7)

2

+(−1)

2

=

50

=5

2

Length of the hypotenuse

AC=

(5−2)

2

+(2+2)

2

=

(3)

2

+(4)

2

=

25

∴AB

2

+AC

2

=25+25=50=BC

2

∴ △ ABC is a right-angled triangle

Area of the triangle ABC

=

2

1

[x

1

(y

2

−y

3

)+x

2

(y

3

−y

1

)+x

3

(y

1

−y

2

)]sq.

Area of the △ABC

=

2

1

×Base×height

=

2

1

×5×5

=

2

25

sq.units