Advertisements
Advertisements
प्रश्न
Find the length of the perpendicular and the co-ordinates of the foot of the perpendicular from (−10, −2) to the line x + y − 2 = 0
उत्तर
The coordinate of the foot of the perpendicular from the point (x1, y1) on the line ax + by + c = 0 is
`(x - x_1)/"a" = (y - y_1)/"b"`
= `- ("a"x_1 + "b"y_1 + "c")/("a"^2 + "b"^2)`
∴ The coordinate of the foot of the perpendicular from the point (– 10, – 2) on the line x + y – 2 = 0 is
`(x + 10)/1 = (y + 2)/1`
= `- (10 - 2 - 2)/(1^2 + 1^2)`
x + 10 = y + 2 = `14/2`
x + 10 = y + 2 = 7
x + 10 = 7, y + 2 = 7
x = – 3, y = 5
∴ The required foot of the perpendicular is (– 3, 5).
Length of the perpendicular
= `sqrt((- 10 + 3)^2 + (- 2 - 5)^2`
= `sqrt((- 7)^2 + (- 7)^2`
= `sqrt(49 + 49)`
= `sqrt(2 xx 49)`
= `7sqrt(2)` units
APPEARS IN
संबंधित प्रश्न
Show that the lines are 3x + 2y + 9 = 0 and 12x + 8y − 15 = 0 are parallel lines
Find the distance between the line 4x + 3y + 4 = 0, and a point (7, −3)
Find the equation of the lines passing through the point of intersection lines 4x − y + 3 = 0 and 5x + 2y + 7 = 0, and parallel to x − y + 5 = 0
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
If p1 and p2 are the lengths of the perpendiculars from the origin to the straight lines x sec θ + y cosec θ = 2a and x cos θ – y sin θ = a cos 2θ, then prove that p12 + p22 = a2
Find the distance between the parallel lines
12x + 5y = 7 and 12x + 5y + 7 = 0
Find the distance between the parallel lines
3x − 4y + 5 = 0 and 6x − 8y − 15 = 0
Find the family of straight lines parallel to 3x + 4y – 12
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
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
A photocopy store charges ₹ 1.50 per copy for the first 10 copies and ₹ 1.00 per copy after the 10th copy. Let x be the number of copies, and let y be the total cost of photocopying. Draw graph of the cost as x goes from 0 to 50 copies
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:
If the two straight lines x + (2k − 7)y + 3 = 0 and 3kx + 9y − 5 = 0 are perpendicular then the value of k is
Choose the correct alternative:
θ is acute angle between the lines x2 – xy – 6y2 = 0 then `(2costheta + 3sintheta)/(4costheta + 5costheta)`
