A straight connecting street segment is built perpendicular to an existing street with equation y = 2 7 x + 3 . Determine the equation of the line of the new street segment, which passes through point B ( - 1 , - 0 . 2 ) .

Given that two streets are perpendicular to each other. The equation of street 1 is given by y = 2 7 x + 3 . . . . i We need to find the equation of street 2 (say) which passes through the point B - 1 , - 0 . 2 , and perpendicular to street 1 . Now, we observe that the equation i is of the form, y = m x + c , where m = gradient of the line, and c = y -intercept of the line. Thus, gradient of street 1 = 2 7 Since street 1 is perpendicular to street 2 ⇒ Gradient of street 1 × Gradient of street 2 = - 1 ⇒ 2 7 × Gradient of street 2 = - 1 ⇒ Gradient of street 2 = - 7 2 . Now, equation of the line with gradient m , and passing through a point x 1 , y 1 is given by y - y 1 = m x - x 1 Thus, equation of street 2 is given by y - - 0 . 2 = - 7 2 x - - 1 ⇒ y + 0 . 2 = - 7 2 x + 1 ⇒ y + 0 . 2 = - 7 2 x - 7 2 ⇒ y = - 7 2 x - 7 2 - 0 . 2 ⇒ y = - 7 2 x - 3 . 5 - 0 . 2 ⇒ y = - 7 2 x - 3 . 7 , which is the required equation of the new street.

A straight connecting street segment is built perpendicular to an existing street with equation y = 2 7 x + 3 . Determine the equation of the line of the new street segment, which passes through point B ( - 1 , - 0 . 2 ) .

Given that two streets are perpendicular to each other. The equation of street 1 is given by y = 2 7 x + 3 . . . . i We need to find the equation of street 2 (say) which passes through the point B - 1 , - 0 . 2 , and perpendicular to street 1 . Now, we observe that the equation i is of the form, y = m x + c , where m = gradient of the line, and c = y -intercept of the line. Thus, gradient of street 1 = 2 7 Since street 1 is perpendicular to street 2 ⇒ Gradient of street 1 × Gradient of street 2 = - 1 ⇒ 2 7 × Gradient of street 2 = - 1 ⇒ Gradient of street 2 = - 7 2 . Now, equation of the line with gradient m , and passing through a point x 1 , y 1 is given by y - y 1 = m x - x 1 Thus, equation of street 2 is given by y - - 0 . 2 = - 7 2 x - - 1 ⇒ y + 0 . 2 = - 7 2 x + 1 ⇒ y + 0 . 2 = - 7 2 x - 7 2 ⇒ y = - 7 2 x - 7 2 - 0 . 2 ⇒ y = - 7 2 x - 3 . 5 - 0 . 2 ⇒ y = - 7 2 x - 3 . 7 , which is the required equation of the new street.

MEDIUM

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A straight connecting street segment is built perpendicular to an existing street with equation $y = \frac{2}{7} x + 3$ . Determine the equation of the line of the new street segment, which passes through point $B (- 1, - 0.2)$ .

Important Questions on Straight Lines

HARD

Mathematics>Coordinate Geometry>Straight Lines>General Equation of a Line

The tangent to the curve

y = x^{2} - 5 x + 5

, parallel to the line

2 y = 4 x + 1

, also passes through the point :

HARD

Mathematics>Coordinate Geometry>Straight Lines>General Equation of a Line

If the straight line

2 x - 3 y + 17 = 0

is perpendicular to the line passing through the points

(7, 17)

and

(15, β)

, then

β

equals :

MEDIUM

Mathematics>Coordinate Geometry>Straight Lines>General Equation of a Line

The number of values of $k$ , for which the system of equations :

$(k + 1) x + 8 y = 4 k$

$k x + (k + 3) y = 3 k - 1$

has no solution, is :

EASY

Mathematics>Coordinate Geometry>Straight Lines>General Equation of a Line

Distance between two parallel lines

y = 2 x + 4

and

y = 2 x - 1

MEDIUM

Mathematics>Coordinate Geometry>Straight Lines>General Equation of a Line

A ray of light along

x + \sqrt{3} y = \sqrt{3}

gets reflected upon reaching

X -

axis, the equation of the reflected ray is

HARD

Mathematics>Coordinate Geometry>Straight Lines>General Equation of a Line

Let

L

be the line passing through the point

P (1, 2)

such that its intercepted segment between the co-ordinate axes is bisected at

P

. If

L_{1}

is the line perpendicular to

L

and passing through the point

(- 2, 1)

, then the point of intersection of

L

and

L_{1}

MEDIUM

Mathematics>Coordinate Geometry>Straight Lines>General Equation of a Line

Two sides of a parallelogram are along the lines,

x + y = 3

and

x - y + 3 = 0 .

If its diagonals intersect at

(2, 4),

then one of its vertex is:

MEDIUM

Mathematics>Coordinate Geometry>Straight Lines>General Equation of a Line

a, b

are positive real numbers such that the lines

a x + 9 y = 5 a n d 4 x + b y = 3

are parallel, then the least possible value of

a + b

EASY

Mathematics>Coordinate Geometry>Straight Lines>General Equation of a Line

Lines are drawn parallel to the line

4 x - 3 y + 2 = 0,

at a distance

\frac{3}{5}

units from the origin. Then which one of the following points lies on any of these lines?

EASY

Mathematics>Coordinate Geometry>Straight Lines>General Equation of a Line

The reflection of the point

(α, β, γ)

in the

x y -

plane is

EASY

Mathematics>Coordinate Geometry>Straight Lines>General Equation of a Line

The equation of the line passing through

(a, b)

and parallel to the line

\frac{x}{a} + \frac{y}{b} = 1

MEDIUM

Mathematics>Coordinate Geometry>Straight Lines>General Equation of a Line

Let

a, b, c

and

d

be non-zero numbers. If the point of intersection of the lines

4 a x + 2 a y + c = 0 & 5 b x + 2 b y + d = 0

lies in the fourth quadrant and is equidistant from the two axes then

HARD

Mathematics>Coordinate Geometry>Straight Lines>General Equation of a Line

For $a > b > c > 0$ , the distance between $(1, 1)$ and the point of intersection of the lines $a x + b y + c = 0$ and $b x + a y + c = 0$ is less than $2 \sqrt{2}$ . Then

HARD

Mathematics>Coordinate Geometry>Straight Lines>General Equation of a Line

A straight line

L

through the point

(3, - 2)

is inclined at an angle of

60 °

to the line

\sqrt{3} x + y = 1 .

L

also intersects the

X

-axis, then the equation of

L

is:

MEDIUM

Mathematics>Coordinate Geometry>Straight Lines>General Equation of a Line

The point on the line

4 x - y - 2 = 0

which is equidistant from the points

(- 5, 6)

and

(3, 2)

is-

HARD

Mathematics>Coordinate Geometry>Straight Lines>General Equation of a Line

Given three points

P, Q, R

with

P (5, 3)

and

R

lies on the

x -

axis. If the equation of

R Q

x - 2 y = 2

and

P Q

is parallel to the

x -

axis, then the centroid of

Δ P Q R

lies on the line

HARD

Mathematics>Coordinate Geometry>Straight Lines>General Equation of a Line

The line which is parallel to

x

-axis and crosses the curve

y = \sqrt{x}

at an angle

45 °

, is

EASY

Mathematics>Coordinate Geometry>Straight Lines>General Equation of a Line

The two equations are

4 x + 4 k y - 6 = 0

and

x + 6 y - 12 = 0

. Find the value of

k

for which the pair of two linear equations represents the parallel lines.

MEDIUM

Mathematics>Coordinate Geometry>Straight Lines>General Equation of a Line

If the two lines

x + (a - 1) y = 1

and

2 x + a^{2} y = 1, (a \in R - \{0,1\})

are perpendicular, then the distance of their point of intersection from the origin is

MEDIUM

Mathematics>Coordinate Geometry>Straight Lines>General Equation of a Line

Two vertices of a triangle are

(0, 2)

and

(4, 3) .

If its orthocenter is at the origin, then its third vertex lies in which quadrant?

A straight connecting street segment is built perpendicular to an existing street with equation y=27x+3. Determine the equation of the line of the new street segment, which passes through point B(-1,-0.2).

Important Questions on Straight Lines

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A straight connecting street segment is built perpendicular to an existing street with equation $y = \frac{2}{7} x + 3$ . Determine the equation of the line of the new street segment, which passes through point $B (- 1, - 0.2)$ .