Advertisements
Advertisements
Question
If the line joining two points A(2, 0) and B(3, 1) is rotated about A in anticlockwise direction through an angle of 15°, then find the equation of the line in new position
Advertisements
Solution
Slope of the line AB
m = tan θ = `(1 - 0)/(3 - 2)`
tan θ = 1
θ = 45°
∴ The line AB makes an angle 45° with x-axis.
Given that the line AB is rotated through an angle of 15° about the point A in the anticlockwise direction.
∴ The angle made by the new line AB’ is 45° + 15° = 60°
Slope of the new line AB’ is m1 = tan 60° = `sqrt(3)`
∴ The equation of the new line AB’ is the equation of the straight line passing through the point A(2, 0) and having slope m1 = `sqrt(3)`
y – 0 = `sqrt(3) (x - 2)`
y = `sqrt(3)x - 2sqrt(3)`
`sqrt(3)x - y - 2sqrt(3)` = 0
APPEARS IN
RELATED QUESTIONS
Find the equation of the straight line parallel to 5x − 4y + 3 = 0 and having x-intercept 3
Find the distance between the line 4x + 3y + 4 = 0, and a point (−2, 4)
Find the distance between the line 4x + 3y + 4 = 0, and a point (7, −3)
Write the equation of the lines through the point (1, −1) parallel to x + 3y − 4 = 0
Write the equation of the lines through the point (1, −1) perpendicular to 3x + 4y = 6
If (−4, 7) is one vertex of a rhombus and if the equation of one diagonal is 5x − y + 7 = 0, then find the equation of another diagonal
Find the equation of the lines passing through the point of intersection lines 4x − y + 3 = 0 and 5x + 2y + 7 = 0, and through the point (−1, 2)
Find the equation of a straight line parallel to 2x + 3y = 10 and which is such that the sum of its intercepts on the axes is 15
Find the family of straight lines perpendicular
Find the family of straight lines parallel to 3x + 4y – 12
A line is drawn perpendicular to 5x = y + 7. Find the equation of the line if the area of the triangle formed by this line with co-ordinate axes is 10 sq.units
Find atleast two equations of the straight lines in the family of the lines y = 5x + b, for which b and the x-coordinate of the point of intersection of the lines with 3x − 4y = 6 are integers
Choose the correct alternative:
The slope of the line which makes an angle 45° with the line 3x − y = −5 are
Choose the correct alternative:
The equation of the line with slope 2 and the length of the perpendicular from the origin equal to `sqrt(5)` is
Choose the correct alternative:
A line perpendicular to the line 5x − y = 0 forms a triangle with the coordinate axes. If the area of the triangle is 5 sq.units, then its equation is
Choose the correct alternative:
θ is acute angle between the lines x2 – xy – 6y2 = 0 then `(2costheta + 3sintheta)/(4costheta + 5costheta)`
