Advertisements
Advertisements
प्रश्न
Answer the following question:
Find the distance of the line 4x − y = 0 from the point P(4, 1) measured along the line making an angle of 135° with the positive X-axis
उत्तर
Let a line L make an angle 135° with positive X-axis.
Required distance = PQ,
where PQ || line L
Slope of PQ = tan135°
= tan(180° – 45°)
= – tan 45°
= – 1
Equation of PQ is
y – 1 = (– 1)(x – 4)
∴ y – 1 = – x + 4
∴ x + y = 5 ...(i)
To get point Q we solve the equation
4x – y = 0 with (i)
Substituting y = 4x in (i), we get
5x = 5
∴ x = 1
Substituting x = 1 in (i), we get
1 + y = 5
∴ y = 4
∴ Q = (1, 4)
PQ = `sqrt((4 - 1)^2 + (1 - 4)^2`
= `sqrt(9 + 9)`
= `3sqrt(2)`
APPEARS IN
संबंधित प्रश्न
Find the slope, X-intercept, Y-intercept of the following line:
2x + 3y – 6 = 0
Find the slope, X-intercept, Y-intercept of the following line:
x + 2y = 0
Write the following equation in ax + by + c = 0 form.
y = 2x – 4
Write the following equation in ax + by + c = 0 form.
y = 4
Write the following equation in ax + by + c = 0 form.
`x/2 + y/4` = 1
Write the following equation in ax + by + c = 0 form.
`x/3 - y/2` = 0
Show that lines x – 2y – 7 = 0 and 2x − 4y + 15 = 0 are parallel to each other
Show that lines x − 2y − 7 = 0 and 2x + y + 1 = 0 are perpendicular to each other. Find their point of intersection
If the line 3x + 4y = p makes a triangle of area 24 square unit with the co-ordinate axes then find the value of p.
Find the co-ordinates of the foot of the perpendicular drawn from the point A(–2, 3) to the line 3x – y – 1 = 0
Find the co-ordinates of the orthocenter of the triangle whose vertices are A(3, –2), B(7, 6), C(–1, 2).
Show that lines 3x − 4y + 5 = 0, 7x − 8y + 5 = 0, and 4x + 5y − 45 = 0 are concurrent. Find their point of concurrence
Find the equation of the line whose X-intercept is 3 and which is perpendicular to the line 3x − y + 23 = 0.
Find the distance of the origin from the line 7x + 24y – 50 = 0
Find the distance between parallel lines 9x + 6y − 7 = 0 and 3x + 2y + 6 = 0
Find the equation of the line passing through the point of intersection of lines x + y − 2 = 0 and 2x − 3y + 4 = 0 and making intercept 3 on the X-axis
If A(4, 3), B(0, 0), and C(2, 3) are the vertices of ∆ABC then find the equation of bisector of angle BAC.
Select the correct option from the given alternatives:
If A(1, −2), B(−2, 3) and C(2, −5) are the vertices of ∆ABC, then the equation of the median BE is
Answer the following question:
Which of the following lines passes through the origin?
Answer the following question:
Obtain the equation of the line which is parallel to the Y−axis and 2 units to the left of it.
Answer the following question:
Obtain the equation of the line which is parallel to the X−axis and making an intercept of 5 on the Y−axis.
Answer the following question:
Find the distance of the origin from the line 12x + 5y + 78 = 0
Answer the following question:
Find the distance of P(−1, 1) from the line 12(x + 6) = 5(y − 2)
Answer the following question:
Find points on the X-axis whose distance from the line `x/3 + y/4` = 1 is 4 unit
For the lines 5x + 2y = 8 and 5x - 2y = 7, which of the following statement is true?
The y-intercept of the line passing through A( 6, 1) and perpendicular to the line x - 2y = 4 is ______.
Let the straight line x = b divide the area enclosed by y = (1 - x)2, y = 0 and x = 0 into two parts R1(0 ≤ x ≤ b) and R2 (b ≤ x ≤ 1) such that `R_1 - R_2 = 1/4`. Then b equals ______
The equation 12x2 + 7xy + ay2 + 13x - y + 3 = 0 represents a pair of perpendicular lines. Then the value of 'a' is ______
The equation 3x2 - 4xy + y2 = 0 represent a pair of straight lines whose slopes differ by ______.
If a plane has x-intercept l, y-intercept m and z-intercept n, and perpendicular distance of plane from the origin is k, then _______.
The length of the perpendicular from the origin on the line `(xsinalpha)/"b" - (ycosalpha)/"a" - 1 = 0` is ______.
If the distance of the point (1, 1, 1) from the origin is half its distance from the plane x + y + z + k = 0, then k = ______.
Find the distance of the origin from the line 7x + 24y – 50 = 0 is:
