# EXERCISE 4.3 (Determinants)

Question 1: Find area of the triangle with vertices at the point given in each of the following:(Class 12 ncert solution math exercise 4.3 determinants)

(i)

(ii)

(iii)

Solution: (i) The area of the triangle with vertices is given by the relation,

Hence, area of the triangle is square units.

(ii) The area of the triangle with vertices is given by the relation,

Hence, area of the triangle is square units.

(iii) The area of the triangle with vertices is given by the relation,

Hence, area of the triangle is 15 square units.

Question 2: Show that the points are collinear.

Solution: The area of the triangle with vertices is given by the absolute value of the relation:

Thus, the area of the triangle formed by points is zero.

Hence, the points are collinear.

Question 3: Find values of if area of triangle is 4 square units and vertices are:

(i)

(ii)

Solution: We know that the area of a triangle whose vertices are and is the absolute value of the determinant , where

It is given that the area of triangle is 4 square units.

Hence,

(i) The area of the triangle with vertices is given by the relation,

Therefore,

When

Then

When

Then

Hence,

(ii) The area of the triangle with vertices is given by the relation,

Therefore,

When

Then

When

Then

Hence,

Question 4: (i) Find equation of line joining and using determinants.

(ii) Find equation of line joining and using determinants.

Solution: (i) Let be any point on the line joining points and .

Then, the points and are collinear.

Hence, the area of triangle will be zero.

Therefore,

Thus, the equation of the line joining the given points is .

(ii) Let be any point on the line joining points and .

Then, the points and are collinear.

Hence, the area of triangle will be zero.

Therefore,

Thus, the equation of the line joining the given points is .

Question 5: If area of the triangle is 35 square units with vertices . Then is
(A) 12
(B)
(C)
(D)

Solution: The area of the triangle with vertices is given by the relation,

It is given that the area of the triangle is 35 square units

Hence, .

Therefore,

When,

Then,

When,

Then,

Hence,

Thus, the correct option is D.