Class 11: The Straight Line

$\displaystyle \textbf{Question 1: }\text{Find the equation of the line parallel to the }x\text{-axis and passing}$
$\displaystyle \text{through }(3,-5).$
$\displaystyle \text{Answer:}$
$\displaystyle \text{The equation of a line parallel to the }x\text{-axis is }y=k.$
$\displaystyle \text{The line passes through }(3,-5).$
$\displaystyle \therefore k=-5.$
$\displaystyle \therefore \text{The required equation is }y+5=0\text{ or }y=-5.$
$\displaystyle \\$

$\displaystyle \textbf{Question 2: }\text{Find the equation of the line perpendicular to the }x\text{-axis and}$
$\displaystyle \text{having intercept }-2\text{ on the }x\text{-axis.}$
$\displaystyle \text{Answer:}$
$\displaystyle \text{The equation of a line perpendicular to the }x\text{-axis is }x=k.$
$\displaystyle \text{The line passes through }(-2,0).$
$\displaystyle \therefore k=-2.$
$\displaystyle \therefore \text{The required equation is }x+2=0\text{ or }x=-2.$
$\displaystyle \\$

$\displaystyle \textbf{Question 3: }\text{Find the equation of the line parallel to the }x\text{-axis and having}$
$\displaystyle \text{intercept }-2\text{ on the }y\text{-axis.}$
$\displaystyle \text{Answer:}$
$\displaystyle \text{The equation of a line parallel to the }x\text{-axis is }y=k.$
$\displaystyle \text{The line passes through }(0,-2).$
$\displaystyle \therefore k=-2.$
$\displaystyle \therefore \text{The required equation is }y+2=0\text{ or }y=-2.$
$\displaystyle \\$

Question 4: Draw the lines $x=-3, x=2, y = -2, y =3$ and write the coordinates of the vertices of the square so formed.

Answer: 2021-01-06_11-10-25

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$\displaystyle \textbf{Question 5: }\text{Find the equations of the straight lines which pass through }(4,3)$
$\displaystyle \text{and are respectively parallel and perpendicular to the }x\text{-axis.}$
$\displaystyle \text{Answer:}$
$\displaystyle \text{i) The equation of a line parallel to the }x\text{-axis is }y=k.$
$\displaystyle \text{The line passes through }(4,3).$
$\displaystyle \therefore k=3.$
$\displaystyle \therefore \text{The required equation is }y-3=0\text{ or }y=3.$
$\displaystyle \text{ii) The equation of a line perpendicular to the }x\text{-axis is }x=k.$
$\displaystyle \text{The line passes through }(4,3).$
$\displaystyle \therefore k=4.$
$\displaystyle \therefore \text{The required equation is }x-4=0\text{ or }x=4.$
$\displaystyle \\$

$\displaystyle \textbf{Question 6: }\text{Find the equation of a line which is equidistant from the lines }$
$\displaystyle x=-2\text{ and }x=6.$
$\displaystyle \text{Answer:}$
$\displaystyle \text{The required line passes through the midpoint of }(-2,0)\text{ and }(6,0).$
$\displaystyle \text{Midpoint}=\left(\frac{-2+6}{2},\frac{0+0}{2}\right)=(2,0).$
$\displaystyle \text{The equation of a vertical line is }x=k.$
$\displaystyle \text{The line passes through }(2,0).$
$\displaystyle \therefore k=2.$
$\displaystyle \therefore \text{The required equation is }x-2=0\text{ or }x=2.$
$\displaystyle \\$

$\displaystyle \textbf{Question 7: }\text{Find the equation of a line equidistant from the lines }y=10\text{ and }y=-2.$
$\displaystyle \text{Answer:}$
$\displaystyle \text{The required line passes through the midpoint of }(0,10)\text{ and }(0,-2).$
$\displaystyle \text{Midpoint}=\left(\frac{0+0}{2},\frac{10+(-2)}{2}\right)=(0,4).$
$\displaystyle \text{The equation of a line parallel to the }x\text{-axis is }y=k.$
$\displaystyle \text{The line passes through }(0,4).$
$\displaystyle \therefore k=4.$
$\displaystyle \therefore \text{The required equation is }y-4=0\text{ or }y=4.$
$\displaystyle \\$