Q. 105.0( 4 Votes )

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Answer :

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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