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  • I need help with - If the straight line,is perpendicular to the line passing through the pointsand thenequals : - Co-ordinate geometry - JEE Main

If the straight line, 2x-3y+17=0 is perpendicular to the line passing through the points \left ( 7,17 \right ) and \left ( 15,\beta \right ), then \beta equals : 

  • Option 1)

    5

     

     

     

  • Option 2)

    \frac{35}{3}

  • Option 3)

    -5

  • Option 4)

    -\frac{35}{3}

Answers (1)

best_answer

 

Two – point form of a straight line -

y-y_{1}=\left ( \frac{y_{2}-y_{1}}{x_{2}-x_{1}} \right )(x-x_{1})

 

- wherein

The lines passes through  (x_{1}y_{1})  and  (x_{2}\, y_{2})

 

 

Condition for perpendicular lines -

m_{1}m_{2}= -1

- wherein

Here m_{1},m_{2}  are the slope of perpendicular lines.

 

\\2x -3y + 17 = 0 \\\\ y = \frac{2}{3}x + \frac{17}{3} \\\\ m_1 = \frac{2}{3} \\\\ m _2 = \frac{\beta - 17}{15 - 7} = \frac{\beta -17}{8} \\\\ m_1\times m_2 = -1 \\\\ \frac{2}{3} \times \frac{\beta -17}{8} = -1 \\\\ \Rightarrow \beta = 5


Option 1)

5

 

 

 

Option 2)

\frac{35}{3}

Option 3)

-5

Option 4)

-\frac{35}{3}

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