Question

(i) Find equation of line joining (1, 2) and (3, 6) using determinants (ii) Find equation of line joining (3, 1) and (9, 3) using determinants

Answer 1

(i)

The given points are ( 1,2 )and( 3,6 ).

Let ( x,y ) be the third point on the line.

Three points lie on the same line and do not form a triangle.

So, the formula used to determine the equation of line is,

0= 1 2 | x 1 y 1 1 x 2 y 2 1 x 3 y 3 1 |

Here,

x 1 =x y 1 =y

x 2 =1 y 2 =2

x 3 =3 y 3 =6

Substitute the values in the above formula.

0= 1 2 | x y 1 1 2 1 3 6 1 | 0=[ x( 2−6 )−y( 1−3 )+1( 6−6 ) ] 0=( −2x+y ) 2x−y=0

Thus, the equation of line is,

2x−y=0

(ii)

The given points are ( 3,1 )and( 9,3 ).

Let ( x,y ) be the third point on the line.

Three points lie on the same line and do not form triangle.

So, the formula used to determine the equation of line is,

0= 1 2 | x 1 y 1 1 x 2 y 2 1 x 3 y 3 1 |

Here,

x 1 =x y 1 =y

x 2 =3 y 2 =1

x 3 =9 y 3 =3

Substitute the values in the above formula.

0= 1 2 | x y 1 3 1 1 9 3 1 | 0=[ x( 1−3 )−y( 3−9 )+1( 9−9 ) ] 0=( −2x+6y+0 ) x−3y=0

Thus, the equation of line is,

x−3y=0