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This is one of our many quizzes on Lines on the coordinate plane. Click on this to access more such competitive quizzes on 2D Coordinate Geometry.

Lines on the coordinate plane Quiz 2

mathematics

 Find the slope of the line:  $ \\ $ <img  src="https://cmds-vedantu.s3.ap-southeast-1.amazonaws.com/prod/question-sets/3402ebf0-b534-4df3-b945-9db27e0803409097180166016760552.png"/>

 Apply the formula of slope $ = \dfrac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}}$ and further solve. 

  Use equation $m = \dfrac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}}$, $ \\    \Rightarrow m = \dfrac{{4 - 0}}{{4 + 2}} \\   \Rightarrow m = \dfrac{4}{6} \\   \Rightarrow m = \dfrac{2}{3} \\ $

 Find the equation of the line with the coordinates $\left( {1,4} \right)$ which is parallel to the line with equation $y =  - x + 1$.

 Parallel lines have equal slopes so compare the given equation with $y = mx + b$ and find the slope and then use $m(x - {x_1}) = (y - {y_1})$ to find the equation of the line.

  Comparing equation $y =  - x + 1$ with equation $y = mx + b$ we get: $ \\ $ Slope $ =  - 1$ $ \\ $ Now using $\left( {1,4} \right)$ we get the equation of line as: $ \\    \Rightarrow  - 1\left( {x - 1} \right) = y - 4 \\   \Rightarrow x + y = 5 \\  $ Because the general equation of line is given as $m(x - {x_1}) = (y - {y_1})$ where m is the slope and $({x_1},{y_1})$ is any point on the line.

 Find the equation of line having coordinates $\left( { - 2,2} \right)$ and $\left( {1,1} \right)$.

 Use formula of slope $m = \dfrac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}}$ and apply formula of line $\left( {y - {y_1}} \right) = \left( {\dfrac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}}} \right)\left( {x - {x_1}} \right).$ 

Using formula to find the equation of a line segment using two endpoints we get: $ \\ \left( {y - {y_1}} \right) = \dfrac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}}\left( {x - {x_1}} \right)$, here $({x_1},{y_1}) = (-2,2)$ because this is any point on the given line. $ \\    \Rightarrow y - 2 = \left( {\dfrac{{1 - 2}}{{1 + 2}}} \right)\left( {x + 2} \right) \\   \Rightarrow x + 3y = 4 \\  $

 Find the equation of a line with the coordinate $\left( {6,4} \right)$ which intersect at the midpoint of line whose coordinate points are $\left( {4,3} \right)$ and $\left( {6,5} \right).$

 Apply midpoint formula $\left( {\dfrac{{{x_1} + {x_2}}}{2}.\dfrac{{{y_1} + {y_2}}}{2}} \right)$ and the use $\left( {y - {y_1}} \right) = \dfrac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}}\left( {x - {x_1}} \right)$ where $({x_1},{y_1})$ is any point on the given line. 

 The midpoint of the given line will be: $ \\   \left( {\dfrac{{4 + 6}}{2},\dfrac{{5 + 5}}{2}} \right) \\   \Rightarrow \left( {5,5} \right) \\  $ Now the equation of the line passing through the points $\left( {5,5} \right),\left( {6,4} \right)$ will be: $ \\ \left( {y - {y_1}} \right) = \dfrac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}}\left( {x - {x_1}} \right)$, here $({x_1},{y_1}) = (5,5) \\ \Rightarrow \left( {y - 5} \right) = \left( {\dfrac{{5 - 4}}{{5 - 6}}} \right)\left( {x - 5} \right) \\   \Rightarrow x + y = 10 \\  $

 Find the equation of given line $ \\ $ <img  src="https://cmds-vedantu.s3.ap-southeast-1.amazonaws.com/prod/question-sets/47d73959-5d45-489e-a8d5-d929cdc3c6bf5490695139371207544.png"/>

 First find the slope of the given line using $m = \dfrac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}}$  and then use  $\left( {y - {y_1}} \right) = m\left( {x - x} \right)$ to find the equation of the given line. 

 Consider the given point $\left( {0,0} \right)$ and $\left( {3,4} \right)$ we will find the slope i.e. $ \\ m = \dfrac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}} \Rightarrow \dfrac{4}{3}$ $ \\ $ Now equation of the line will be: $ \\   {\text{(y - }}{{\text{y}}_1}{\text{) = m(x - }}{{\text{x}}_1}{\text{) }} \\   \Rightarrow \left( {y - 0} \right) = \dfrac{4}{3}\left( {x - 0} \right) \\   \Rightarrow 4x - 3y = 0 \\  $