Question

(9, a), (6, 7), (2, 3) are the coordinates of the vertices of a triangle. If the area of the
triangle is 10, find a.
​

Answer 1

Plot the points in a rough diagram and take them in order.

Let the vertices be A(1,2),B(−3,4) and C(−5,−6)

Now the area of △ABC is

=

2

1

{(x

1

y

2

+x

2

y

3

+x

3

y

1

)−(x

2

y

1

+x

3

y

2

+x

1

y

3

)}

=

2

1

{(4+18−10)−(−6−20−6)}

=

2

1

(12+32)=22 sq.units.