The points A(2, 3), B(4, -1) and C(-1, 2) are the vertices of ΔABC. Find the length of the perpendicular from C on AB and hence find the area of ΔABC

Given: points A(2, 3), B(4, -1) and C(-1, 2) are the vertices of ΔABC

To find : length of the perpendicular from C on AB and the area of ΔABC

Formula used:

We know that the length of the perpendicular from (m,n) to the line ax + by + c = 0 is given by,

D

The equation of the line joining the points (x₁,y₁) and (x₂,y₂) is given by

The equation of the line joining the points A(2,3) and B(4,-1) is

Here x₁ =2 y₁ =3 and x₂=4 y₂=-1

The equation of the line is 2x + y – 7 =0

The length of perpendicular from C(-1, 2) to the line AB

The given equation of the line is 2x + y – 7 =0

Here m= -1 and n= 2 , a = 2 , b = 1 , c = -7

D

D

D

The length of the perpendicular from C on AB is units.

Height of the triangle is units

The distance between points A(x₁, y₁) and B(x₂, y₂) is given by

AB =

Here x1=2 and y1=3 ,x2=4 and y2=-1

AB =

Base AB = units

Area of the triangle =

Area of the triangle ABC =

Area of the triangle ABC = 7 square units