Advertisements
Advertisements
Question
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.
Advertisements
Solution
Given equation of the line is 3x + 2y = 2.
∴ `(3x)/2 + (2y)/2` = 1
∴ `x/(2/3) + y/1` = 1
This equation is of the form `x/"a" + y/"b"` = 1, with a = `2/3`, b = 1.
∴ The line 3x + 2y = 2 intersects the X-axis at A `(2/3, 0)` and Y-axis at B(0, 1).
The required line is passing through the midpoint of AB.
∴ Midpoint of AB = `((2/3 + 0)/2, (0 + 1)/2) = (1/3, 1/2)`
∴ Required line passes through (0, 0) and `(1/3, 1/2)`.
Equation of the line in two point form is
`(y - y_1)/(y_2 - y_1) = (x - x_1)/(x_2 - x_1)`
∴ The equation of the required line is
`(y - 0)/(1/2 - 0) = (x - 0)/(1/3 - 0)`
∴ 2y = 3x
∴ 3x – 2y = 0
APPEARS IN
RELATED QUESTIONS
Write the equation of the line :
parallel to the X-axis and at a distance of 4 unit form the point (−2, 3)
Obtain the equation of the line :
parallel to the Y−axis and making an intercept of 4 unit on the X−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 passing through the points P(2, 1) and Q(2, –1)
Find the equation of the line containing the origin and having inclination 60°
Find the equation of the line passing through the origin and parallel to AB, where A is (2, 4) and B is (1, 7)
Find the equation of the line containing point A(3, 5) and having slope `2/3`.
Find the equation of the line containing point A(4, 3) and having inclination 120°
Line y = mx + c passes through points A(2, 1) and B(3, 2). Determine m and c.
The vertices of a triangle are A(3, 4), B(2, 0), and C(−1, 6). Find the equation of the line containing the median AD
Find the x and y intercept of the following line:
`x/3 + y/2` = 1
Find equations of lines containing the point A(3, 4) and making equal intercepts on the co-ordinates axes.
Find equations of altitudes of the triangle whose vertices are A(2, 5), B(6, –1) and C(–4, –3).
N(3, −4) is the foot of the perpendicular drawn from the origin to line L. Find the equation of line L.
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"` =
Answer the following question:
Obtain the equation of the line containing the point (2, 3) and parallel to the X-axis.
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 passing through the points S(2, 1) and T(2, 3)
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:
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 Y-intercept of the line whose slope is 4 and which has X intercept 5
Answer the following question:
Find the co-ordinates of the foot of the perpendicular drawn from the point P(−1, 3) the line 3x − 4y − 16 = 0
Answer the following question:
The perpendicular from the origin to a line meets it at (−2, 9). Find the equation of the line.
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 ____________.
The slope of normal to the curve x = `sqrt"t"` and y = `"t" - 1/sqrt"t"`at t = 4 is _____.
The point A(b, a) lies on the straight line 2x + 3y = 13 and the point B(a, b) lies on the straight line -x + 4y = 5, then the equation of line AB is ______
The line L given by `x/5+y/b=1` passes through the point (13, 32). The line K is parallel to L and its equation is `x/c+y/3=1`. Then, the distance between L and K is ______.
The angle between the lines x sin 60° + y cos 60° = 5 and x sin 30° + y cos 30° = 7 is ______
Suppose the line `(x - 2)/α = ("y" - 2)/(-5) = ("z" + 2)/2` lies on the plane x + 3y – 2z + β = 0. Then (α + β) is equal to ______.
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 ______.
