$
{\text{Find the equation of the line passing through the point }}\left( { - 4, - 3} \right){\text{ and perpendicular to the straight }} \\
{\text{line joining }}\left( {1,3} \right){\text{ and }}\left( {2,7} \right). \\
$
Answer
370.2k+ views

$
{\text{Now, we have to find the equation of line passing through point }}P\left( { - 4, - 3} \right){\text{ and perpendicular}} \\
{\text{to the line joining the given points}}{\text{.}} \\
{\text{First we find slope of line formed after joining two points Q}}\left( {1,3} \right){\text{ and }}R\left( {2,7} \right){\text{.}} \\
{\text{Let slope of line joining points Q}}\left( {1,3} \right){\text{ and }}R\left( {2,7} \right){\text{ be }}{m_1}{\text{.}} \\
{\text{Them }}{m_1} = \dfrac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}} = \dfrac{{7 - 3}}{{2 - 1}} = 4 \\
{\text{Let the slope of required line be }}{m_2} \\
{\text{As, it is give that the required line is perpendicular to the line joining points Q}}\left( {1,3} \right){\text{ and }}R\left( {2,7} \right). \\
{\text{So, }}{m_1}*{m_2} = - 1 \\
{\text{Putting value of }}{m_1}{\text{, we get }}{m_2} = \dfrac{{ - 1}}{4} \\
{\text{Now, finding the equation of line passing through point P and having slope }}{m_2}{\text{ using point slope form,}} \\
\left( {y - \left( { - 3} \right)} \right) = \dfrac{{ - 1}}{4}\left( {x - \left( { - 4} \right)} \right){\text{ }}\left( 1 \right) \\
{\text{Cross - multiplying equation 1 we get,}} \\
4y + 12 = - x - 4 \\
{\text{Solving above equation we get }}4y + x + 16 = 0 \\
{\text{Hence, equation of line passing through point P and perpendicular to line joining points Q and R}} \\
{\text{is }}4y + x + 16 = 0 \\
{\text{NOTE: - Whenever you come up with a type of problem the first find the slope of lines}}{\text{. As for}} \\
{\text{perpendicular lines }}{m_1}*{m_2} = - 1{\text{ and for parallel line }}{m_1} = {m_2}{\text{. Then use point - slope form to }} \\
{\text{find equation of line}}{\text{.}} \\
$
Last updated date: 28th Sep 2023
•
Total views: 370.2k
•
Views today: 10.70k
Recently Updated Pages
What do you mean by public facilities

Paragraph on Friendship

Slogan on Noise Pollution

Disadvantages of Advertising

Prepare a Pocket Guide on First Aid for your School

10 Slogans on Save the Tiger

Trending doubts
How do you solve x2 11x + 28 0 using the quadratic class 10 maths CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Difference Between Plant Cell and Animal Cell

One cusec is equal to how many liters class 8 maths CBSE

The equation xxx + 2 is satisfied when x is equal to class 10 maths CBSE

What is the color of ferrous sulphate crystals? How does this color change after heating? Name the products formed on strongly heating ferrous sulphate crystals. What type of chemical reaction occurs in this type of change.

Give 10 examples for herbs , shrubs , climbers , creepers

Change the following sentences into negative and interrogative class 10 english CBSE
