Q : 10     The line through the points  (h,3)  and  (4,1)  intersects the line 7x-9y-19=0  at right angle. Find the value of  h

Answers (1)
G Gautam harsolia

Line passing through points ( h ,3) and (4 ,1)

Therefore,Slope of the line is

m =\frac{y_2-y_1}{x_2-x_1} 

m =\frac{3-1}{h-4}

This line intersects the line 7x-9y-19=0  at right angle
Therefore, the Slope of both the lines are negative times inverse of each other 
Slope of line 7x-9y-19=0 , m'=\frac{7}{9}
Now,
m=-\frac{1}{m'}
\frac{2}{h-4}= -\frac{9}{7}
14=-9(h-4)
14=-9h+36
-9h= -22
h=\frac{22}{9}
Therefore, the value of h is  \frac{22}{9} 

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