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  • State whether the statements are true or false. Line joining the points (3, – 4) and (– 2, 6) is perpendicular to the line joining the points (–3, 6) and (9, –18).

State whether the statements are true or false.
Line joining the points (3, – 4) and (– 2, 6) is perpendicular to the line joining the points (–3, 6) and (9, –18).

Answers (1)

Given points are (3,-4), (-2,6), (-3,6) and (9,-18) 

  Now we find the slope since the lines are perpendicular, the product of the slopes is -1 i.e. m1m2= -1  

Slope of the line joining the points (3,-4) and (-2,6) 

m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}

  Here, x1=3, x2=-2 , y1=-4 and y2=6   

m_{1}=\frac{6-\left ( -4 \right )}{-2-3}=\frac{6+4}{-5}=\frac{10}{-5}=-2 

 Now, slope of the line joining the points -(3,6) and (9,-18)

m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}

 Here, x1=-3, x2=9, y1=6 and y2=-18  

 m_{2}=\frac{-18-6}{9-(-3)}=\frac{24}{9+3}=-\frac{24}{12}=-2

 m1=m2=-2   

 and m1m2= -2*(-2)=-4 ≠-1   

So, the lines are parallel and not perpendicular   

 Hence, the given statement is False

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