# 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.**