(B) The midpoint of the line segment joining $(1, 3)$ and $(1, -7)$ is given by $\left( \frac{1+1}{2}, \frac{3-7}{2} \right) = (1, -2)$.Since the requ

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(B) The midpoint of the line segment joining $(1, 3)$ and $(1, -7)$ is given by $\left( \frac{1+1}{2}, \frac{3-7}{2} \right) = (1, -2)$.Since the required line is parallel to $2x - 3y = 1$,its equation is of the form $2x - 3y = k$.Substituting the point $(1, -2)$ into the equation: $2(1) - 3(-2) = k$.$2 + 6 = k \Rightarrow k = 8$.Thus,the equation of the line is $2x - 3y = 8$.

Class 11 Mathematics Straight Line Slope of line, Equation of line in different forms

Easy

The equation of the line parallel to the line $2x - 3y = 1$ and passing through the midpoint of the line segment joining the points $(1, 3)$ and $(1, -7)$ is:

A
$2x - 3y + 8 = 0$
B
$2x - 3y = 8$
C
$2x - 3y + 4 = 0$
D
$2x - 3y = 4$

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Class 11

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Straight Line

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Slope of line, Equation of line in different forms

Find the equation of the line perpendicular to the line $2x - 3y = 5$ and passing through the point $(1, -1)$.

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If the coordinates of the points $A, B, C, D$ are $(a, b), (a', b'), (-a, b)$ and $(a', -b')$ respectively,then the equation of the line bisecting the line segments $AB$ and $CD$ is

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Write the equation of the lines for which $\tan \theta = \frac{1}{2}$,where $\theta$ is the inclination of the line and $y$-intercept is $-\frac{3}{2}$.

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Find the equation of the line,which makes intercepts $-3$ and $2$ on the $x$- and $y$-axes respectively.

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The length $L$ (in centimetre) of a copper rod is a linear function of its Celsius temperature $C$. In an experiment,if $L = 124.942$ when $C = 20$ and $L = 125.134$ when $C = 110,$ express $L$ in terms of $C$.

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The equation of the line parallel to the line $2x - 3y = 1$ and passing through the midpoint of the line segment joining the points $(1, 3)$ and $(1, -7)$ is:

Similar Questions

Find the equation of the line perpendicular to the line $2x - 3y = 5$ and passing through the point $(1, -1)$.

If the coordinates of the points $A, B, C, D$ are $(a, b), (a', b'), (-a, b)$ and $(a', -b')$ respectively,then the equation of the line bisecting the line segments $AB$ and $CD$ is

Write the equation of the lines for which $\tan \theta = \frac{1}{2}$,where $\theta$ is the inclination of the line and $y$-intercept is $-\frac{3}{2}$.

Find the equation of the line,which makes intercepts $-3$ and $2$ on the $x$- and $y$-axes respectively.

The length $L$ (in centimetre) of a copper rod is a linear function of its Celsius temperature $C$. In an experiment,if $L = 124.942$ when $C = 20$ and $L = 125.134$ when $C = 110,$ express $L$ in terms of $C$.

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