Suppose that the points (h,k),(1,2) and \left ( -3,4 \right ) lie on the line L_1. If a line L_2 passing through the points \left ( h,k \right ) and \left ( 4,3 \right ) is perpendicular to L_1, then \frac{k}{h} equals: 

  • Option 1)

    \frac{1}{3}

  • Option 2)

    0

  • Option 3)

    3

     

  • Option 4)

    -\frac{1}{7}

Answers (1)


Line L_1 contain points : \left ( h,k \right ),(1,2) and \left ( -3,4 \right )

slope of L_1=\frac{4-2}{-3-1}=-\frac{1}{2}

L_2 is \perp to L_1; so slope of L_2 is 2

Again; slope of L_1=\frac{k-2}{h-1}=-\frac{1}{2}

\Rightarrow 2k-4=-h+1\Rightarrow h+2k=5\cdots (1)

Line L_2 contains point : \left ( h,k \right ),(4,3)

Slope of L_2=\frac{k-3}{h-4}=2\Rightarrow k-3=2h-8

k=2h-5\cdots (II)

solve (1) and (2), (h,k)=(3,1)


Option 1)

\frac{1}{3}

Option 2)

0

Option 3)

3

 

Option 4)

-\frac{1}{7}

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