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