# <span lang="EN-US

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

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