Question

The vertices of ABC are A(2,3), B(-2,1) and C(-1,1)
(a) FInd the lengths of AB, BC and CA
(b) Show that ABC is a right angled triangle
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You will get 50 points if answer this question correctly and carefully

Answer 1

Step-by-step explanation:

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Answer 2

Step-by-step explanation:

Answer

Let A(2,1),B(−2,3),C(4,5) be vertices of △ABC and AD be the median.

D be mid point of BC.

D=(

2

−2+4

,

2

3+5

)

⇒D=(1,4)

Now A(2,1)≡(x

2

,y

2

)andD(1,4)≡(x

1

,y

1

)

The equation of median AD is

y

2

−y

1

y−y

1

=

x

2

−x

1

x−x

1

⇒

1−4

y−4

=

2−1

x−1

⇒

−3

y−4

=

1

x−1

⇒−3x+3=y−4

⇒3x−3+y−4=0

⇒3x+y−7=0