Question

show that the following pairs of lines are perpendicular to each other 2 x - 4y = 5 and 2x+ y= 17​

Answer 1

Answer:

Step-by-step explanation:

Answer 2

The pair of lines 2x - 4y = 5 and 2x + y = 17 are perpendicular to each other

Given :

The pair of lines 2x - 4y = 5 and 2x + y = 17

To find :

To prove pair of lines 2x - 4y = 5 and 2x + y = 17 are perpendicular to each other

Solution :

Step 1 of 3 :

Find slope of the first line

The equation of the first line is

2x - 4y = 5

$\displaystyle \sf{ \implies 4y = 2x - 5}$

$\displaystyle \sf{ \implies y = \frac{1}{2} x - \frac{5}{4} }$

Slope of the first line is given by

$\displaystyle \sf{m_1 = \frac{1}{2} }$

Step 2 of 3 :

Find slope of the second line

Here the given equation of the second line is

2x + y = 17

$\displaystyle \sf{ \implies y = - 2x + 17}$

Slope of the second line is given by

$\displaystyle \sf{m_2 = - 2 }$

Step 3 of 3 :

Prove that the lines are perpendicular

Product of slopes of the two lines

$\displaystyle \sf{ = m_1 \times m_2 }$

$\displaystyle \sf{ = \frac{1}{2} \times ( - 2)}$

$\displaystyle \sf{ = - 1 }$

We know that two lines are said to be perpendicular if product of the slopes of two lines = - 1

Hence the pair of lines 2x - 4y = 5 and 2x + y = 17 are perpendicular to each other

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