The points A(2,9),B(a,5)   and C(5,5)   are the vertices of ΔABC   right angled at B  . Find the value of a   and hence the area of ΔABC   from the following choices is:

# The points   and   are the vertices of   right angled at  . Find the value of   and hence the area of   from the following choices is:

1. A
and Area   square units
2. B
and Area   square units
3. C
and Area   square units
4. D
and Area   square units

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### Solution:

Given that, the points    and  .
The distance formula between two points   is given by,

By using Pythagoras theorem:

Distance between the points AB:
Here,

Distance between the points AB:
Here,

Distance between the points AC:
Here,

Substitute the value in the Pythagoras theorem,
By simplification,

The value of  (2, 5) and the area is   square units.
Hence, option 4) is correct.

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