Advertisements
Advertisements
Question
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)
Solution
Slope of ST = `(5 - 2)/(2 - 1) = 3/1` = 3
Since the required line is perpendicular to ST, the slope of the line is `-1/3` and it is passing through A(–2, 3).
∴ Equation of the line in slope point form is y − y1 = m(x − x1)
∴ The equation of the required line is
y – 3 = `-1/3(x + 2)`
∴ 3(y – 3) = –(x + 2)
∴ 3y – 9 = – x – 2
∴ x + 3y = 7
APPEARS IN
RELATED QUESTIONS
Write the equation of the line :
parallel to the Y−axis and at a distance of 5 unit form it and to the left of it
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 containing point A(4, 3) and having inclination 120°
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.
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.
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
The vertices of a triangle are A(3, 4), B(2, 0), and C(−1, 6). Find the equation of the line containing the midpoints of sides AB and BC
Find the x and y intercept of the following line:
`(3x)/2 + (2y)/3` = 1
Find the x and y intercept of the following line:
2x − 3y + 12 = 0
Find equations of lines which contains the point A(1, 3) and the sum of whose intercepts on the coordinate axes is zero.
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).
Find the coordinates of the orthocenter of the triangle whose vertices are A(2, −2), B(1, 1), and C(−1, 0).
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:
Reduce the equation 6x + 3y + 8 = 0 into slope-intercept form. Hence find its slope
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 which contains the point A(3, 5) and makes equal intercepts on the co-ordinates 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 the medians.
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 X−intercept of the line whose slope is 3 and which makes intercept 4 on the Y−axis
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.
Answer the following question:
The perpendicular from the origin to a line meets it at (−2, 9). Find the equation of the line.
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 ______
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 ______.
Area of the parallelogram formed by the lines y = mx, y = mx + 1, y = nx and y = nx + 1 is equal to ______.
