Advertisements
Advertisements
प्रश्न
Answer the following question:
A line perpendicular to segment joining A(1, 0) and B(2, 3) divides it internally in the ratio 1 : 2. Find the equation of the line.
Advertisements
उत्तर
Let P(x, y) be the point which divides AB internally in the ratio 1 : 2, where A(1, 0) and B(2, 3).
∴ x = `(1(2) + 2(1))/(1 + 2) = (2 + 2)/3 = 4/3`
and y = `(1(3) + 2(0))/(1 + 2) = (3 + 0)/3` = 1
∴ P ≡ `(4/3, 1)`
Now, slope of AB = `(3 - 0)/(2 - 1)` = 3
∴ slope of the line perpendicular to AB is `-1/3` and it is passing through `"P"(4/3, 1)`.
∴ equation of the required line is
y – 1 =`-1/3(x - 4/3)`
∴ 3y – 3 = `- x + 4/3`
∴ x + 3y = `13/3`
∴ 3x + 9y = 13
APPEARS IN
संबंधित प्रश्न
Obtain the equation of the line :
parallel to the X−axis and making an intercept of 3 unit on the Y−axis
Obtain the equation of the line containing the point :
A(2, – 3) and parallel to the Y−axis
Find the equation of the line having slope `1/2` and containing the point (3, −2).
Find the equation of the line passing through the origin and which bisects the portion of the line 3x + y = 6 intercepted between the co-ordinate axes.
Find the equation of the line having inclination 135° and making X-intercept 7
The vertices of a triangle are A(3, 4), B(2, 0), and C(−1, 6). Find the equation of the line containing side BC.
Find the x and y intercept of the following line:
`x/3 + y/2` = 1
Find the x and y intercept of the following line:
2x − 3y + 12 = 0
Find equations of altitudes of the triangle whose vertices are A(2, 5), B(6, –1) and C(–4, –3).
Find the equations of perpendicular bisectors of sides of the triangle whose vertices are P(−1, 8), Q(4, −2), and R(−5, −3)
Select the correct option from the given alternatives:
If the point (1, 1) lies on the line passing through the points (a, 0) and (0, b), then `1/"a" + 1/"b"` =
Select the correct option from the given alternatives:
If the line kx + 4y = 6 passes through the point of intersection of the two lines 2x + 3y = 4 and 3x + 4y = 5, then k =
Answer the following question:
Does point A(2, 3) lie on the line 3x + 2y – 6 = 0? Give reason.
Answer the following question:
Obtain the equation of the line containing the point (2, 4) and perpendicular to the Y−axis
Answer the following question:
Find the equation of the line having slope 5 and containing point A(–1, 2).
Answer the following question:
Find the equation of the line through the origin which bisects the portion of the line 3x + 2y = 2 intercepted between the co−ordinate axes.
Answer the following question:
The vertices of a triangle are A(1, 4), B(2, 3) and C(1, 6). Find equations of the sides.
Answer the following question:
The vertices of a triangle are A(1, 4), B(2, 3) and C(1, 6) Find equations of Perpendicular bisectors of sides
Answer the following question:
Find the equation of the line through A(−2, 3) and perpendicular to the line through S(1, 2) and T(2, 5)
Answer the following question:
Find the X−intercept of the line whose slope is 3 and which makes intercept 4 on the Y−axis
Answer the following question:
Find the Y-intercept of the line whose slope is 4 and which has X intercept 5
Answer the following question:
Find the equations of the diagonals of the rectangle whose sides are contained in the lines x = 8, x = 10, y = 11 and y = 12
Answer the following question:
A(1, 4), B(2, 3) and C(1, 6) are vertices of ∆ABC. Find the equation of the altitude through B and hence find the co-ordinates of the point where this altitude cuts the side AC of ∆ABC.
Answer the following question:
P(a, b) is the mid point of a line segment between axes. Show that the equation of the line is `x/"a" + y/"b"` = 2
Answer the following question:
Show that there are two lines which pass through A(3, 4) and the sum of whose intercepts is zero.
Answer the following question:
Show that there is only one line which passes through B(5, 5) and the sum of whose intercept is zero.
If (a, −2a), a > 0 is the mid-point of a line segment intercepted between the co-ordinate axes, then the equation of the line is ____________.
If for a plane, the intercepts on the co-ordinate axes are 8, 4, 4, then the length of the perpendicular from the origin to the plane is ______
The lines `(x + 1)/(-10) = (y + 3)/-1 = (z - 4)/1` and `(x + 10)/(-1) = (y + 1)/-3 = (z - 1)/4` intersect at the point ______
A Plane cuts the coordinate axes X, Y, Z at A, B, C respectively such that the centroid of the Δ ABC is (6, 6, 3). Then the equation of that plane is ______.
Let the perpendiculars from any point on the line 7x + 56y = 0 upon 3x + 4y = 0 and 5x – 12y = 0 be p and p', then ______.
