Question

what is the answer and what is the formula used ​

Answer 1

QUESTION:

Distance from the origin to the line ax + by + 5 = 0 is 5/√10 then distance from the origin to the line ax + by + 10 equal to zero is.

ANSWER:

• Distance from the origin to the line ax + by + 10 = √10 units.

GIVEN:

• Distance from the origin to the line ax + by + 5 = 0 is 5/√10 units.

TO FIND:

• Distance from the origin to the line ax + by + 10.

EXPLANATION:

$\boxed{\gray{\bold{Distance = \left| \dfrac{ax_{1} +by_{1} + c }{ \sqrt{{a}^{2} + {b}^{2}} } \right|}}}$

D = 5/√10 units

a = a

b = b

c = 5

$x_{1},y_{1} = (0 ,0)$

$\dfrac{5}{\sqrt{10}} = \left|\dfrac{a(0) +b(0) + 5 }{ \sqrt{{a}^{2} + {b}^{2}}}\right|$

$\dfrac{5}{\sqrt{10}} = \dfrac{ 5 }{\sqrt{{a}^{2} + {b}^{2}}}$

$\dfrac{1}{\sqrt{10}} = \dfrac{ 1 }{\sqrt{{a}^{2} + {b}^{2}}}$

$\sqrt{10}= \sqrt{{a}^{2} + {b}^{2}}$

$\boxed{\gray{\bold{Distance = \left| \dfrac{ax_{1} +by_{1} + c }{ \sqrt{{a}^{2} + {b}^{2}} } \right|}}}$

Distance = d

a = a

b = b

c = 10

$d = \left|\dfrac{a(0) +b(0) + 10 }{ \sqrt{{a}^{2} + {b}^{2}}}\right|$

$d = \left|\dfrac {10 }{ \sqrt{{a}^{2} + {b}^{2}}}\right|$

$Substitute \ \sqrt{{a}^{2}+ {b}^{2}}=\sqrt{10}$

$d = \dfrac {10 }{ \sqrt{10}}$

d = √10 units.

Hence the distance from the origin to the line ax + by + 10 is√10 units.

NOTE : REFER ATTACHMENT FOR DIAGRAM.