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Q : 5         If the area of triangle is 35 sq units with vertices  $\small (2,-6),(5,4)$  and $\small (k,4)$. Then k is

(A) $\small 12$      (B) $\small -2$     (C) $\small -12,-2$       (D) $\small 12,-2$

Area of triangle is given by: or    or    Hence the possible values of k are 12 and -2. Therefore option (D) is correct.

Q : 4         (ii) Find equation of line joining $\small (3,1)$ and $\small (9,3)$ using determinants.

We can find the equation of the line by considering any arbitrary point  on line. So, we have three points which are collinear and therefore area surrounded by them will be equal to zero. Calculating the determinant: Hence we have the line equation:   or  .

Q : 4       (i)  Find equation of line joining $\small (1,2)$ and $\small (3,6)$ using determinants.

As we know the line joining  ,  and let say a point on line  will be collinear.   Therefore area formed by them will be equal to zero. So, we have: or  Hence, we have the equation of line .

Q : 3       Find values of k if area of triangle is 4 sq. units and vertices are

(ii)   $(-2,0), (0,4), (0,k)$

The area of the triangle is given by the formula: Now, calculating the area: or           Therefore we have two possible values of 'k' i.e.,    or  .

Q : 3          Find values of k if area of triangle is 4 sq. units and vertices are

(i) $(k,0), (4,0), (0,2)$

We can easily calculate the area by the formula :                                    or    or      or   Hence two values are possible for k.

Q: 2           Show that points  $A (a, b+c), B (b,c+a), C (c,a+b)$  are collinear.

If the area formed by the points is equal to zero then we can say that the points are collinear. So, we have an area of a triangle given by, calculating the area: Hence the area of the triangle formed by the points is equal to zero. Therefore given points  are collinear.

1    Find area of the triangle with vertices at the point given in each of the following :

(iii) $(-2,-3), (3,2), (-1,-8)$

Area of the triangle by the determinant method: Hence the area is equal to

Q : 1         Find area of the triangle with vertices at the point given in each of the following :

(ii) $(2,7), (1,1), (10,8)$

We can find the area of the triangle with given coordinates by the following method:

Q : 1          Find area of the triangle with vertices at the point given in each of the following :

(i)  $(1,0), (6,0), (4,3)$

We can find the area of the triangle with vertices  by the following determinant relation: Expanding using second column
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