Advertisements
Advertisements
Question
Find the equation of the perpendicular to the line segment joining (4, 3) and (−1, 1) if it cuts off an intercept −3 from y-axis.
Advertisements
Solution
Let m be the slope of the required line.
Here, c = y-intercept = \[-\] 3
Slope of the line joining the points (4, 3) and (−1, 1) = \[\frac{1 - 3}{- 1 - 4} = \frac{2}{5}\]
It is given that the required line is perpendicular to the line joining the points (4, 3) and (−1, 1).
\[\therefore m \times \text { Slope of the line joining the points } \left( 4, 3 \right) and \left( - 1, 1 \right) = - 1\]
\[ \Rightarrow m \times \frac{2}{5} = - 1\]
\[ \Rightarrow m = \frac{- 5}{2}\]
Substituting the values of m and c in y = mx + c, we get:
\[y = - \frac{5}{2}x - 3 \]
\[ \Rightarrow 5 x + 2y + 6 = 0\]
Hence, the equation of the required line is 5x + 2y + 6 = 0.
APPEARS IN
RELATED QUESTIONS
Find the distance between P (x1, y1) and Q (x2, y2) when :
- PQ is parallel to the y-axis,
- PQ is parallel to the x-axis
The slope of a line is double of the slope of another line. If tangent of the angle between them is `1/3`, find the slopes of the lines.
A line passes through (x1, y1) and (h, k). If slope of the line is m, show that k – y1 = m (h – x1).
Find the value of p so that the three lines 3x + y – 2 = 0, px + 2y – 3 = 0 and 2x – y – 3 = 0 may intersect at one point.
Find the slope of the lines which make the following angle with the positive direction of x-axis:
\[\frac{3\pi}{4}\]
Find the slope of a line passing through the following point:
(−3, 2) and (1, 4)
Find the slope of a line passing through the following point:
\[(a t_1^2 , 2 a t_1 ) \text { and } (a t_2^2 , 2 a t_2 )\]
What can be said regarding a line if its slope is zero ?
Show that the line joining (2, −3) and (−5, 1) is parallel to the line joining (7, −1) and (0, 3).
Prove that the points (−4, −1), (−2, −4), (4, 0) and (2, 3) are the vertices of a rectangle.
If three points A (h, 0), P (a, b) and B (0, k) lie on a line, show that: \[\frac{a}{h} + \frac{b}{k} = 1\].
Consider the following population and year graph:
Find the slope of the line AB and using it, find what will be the population in the year 2010.
Find the angle between X-axis and the line joining the points (3, −1) and (4, −2).
Find the equation of a straight line with slope −2 and intersecting the x-axis at a distance of 3 units to the left of origin.
Find the equations of the bisectors of the angles between the coordinate axes.
Find the equation of the right bisector of the line segment joining the points (3, 4) and (−1, 2).
Find the angles between the following pair of straight lines:
3x + 4y − 7 = 0 and 4x − 3y + 5 = 0
Prove that the straight lines (a + b) x + (a − b ) y = 2ab, (a − b) x + (a + b) y = 2ab and x + y = 0 form an isosceles triangle whose vertical angle is 2 tan−1 \[\left( \frac{a}{b} \right)\].
The acute angle between the medians drawn from the acute angles of a right angled isosceles triangle is
The equation of the line with slope −3/2 and which is concurrent with the lines 4x + 3y − 7 = 0 and 8x + 5y − 1 = 0 is
The coordinates of the foot of the perpendicular from the point (2, 3) on the line x + y − 11 = 0 are
Find k, if the slope of one of the lines given by kx2 + 8xy + y2 = 0 exceeds the slope of the other by 6.
If m1 and m2 are slopes of lines represented by 6x2 - 5xy + y2 = 0, then (m1)3 + (m2)3 = ?
If x + y = k is normal to y2 = 12x, then k is ______.
The two lines ax + by = c and a′x + b′y = c′ are perpendicular if ______.
Find the angle between the lines y = `(2 - sqrt(3)) (x + 5)` and y = `(2 + sqrt(3))(x - 7)`
Find the equation of a straight line on which length of perpendicular from the origin is four units and the line makes an angle of 120° with the positive direction of x-axis.
The equation of the straight line passing through the point (3, 2) and perpendicular to the line y = x is ______.
The tangent of angle between the lines whose intercepts on the axes are a, – b and b, – a, respectively, is ______.
The coordinates of the foot of perpendiculars from the point (2, 3) on the line y = 3x + 4 is given by ______.
Equations of diagonals of the square formed by the lines x = 0, y = 0, x = 1 and y = 1 are ______.
The point (4, 1) undergoes the following two successive transformations:
(i) Reflection about the line y = x
(ii) Translation through a distance 2 units along the positive x-axis Then the final coordinates of the point are ______.
The points (3, 4) and (2, – 6) are situated on the ______ of the line 3x – 4y – 8 = 0.
Line joining the points (3, – 4) and (– 2, 6) is perpendicular to the line joining the points (–3, 6) and (9, –18).
| Column C1 | Column C2 |
| (a) The coordinates of the points P and Q on the line x + 5y = 13 which are at a distance of 2 units from the line 12x – 5y + 26 = 0 are |
(i) (3, 1), (–7, 11) |
| (b) The coordinates of the point on the line x + y = 4, which are at a unit distance from the line 4x + 3y – 10 = 0 are |
(ii) `(- 1/3, 11/3), (4/3, 7/3)` |
| (c) The coordinates of the point on the line joining A (–2, 5) and B (3, 1) such that AP = PQ = QB are |
(iii) `(1, 12/5), (-3, 16/5)` |
The line which passes through the origin and intersect the two lines `(x - 1)/2 = (y + 3)/4 = (z - 5)/3, (x - 4)/2 = (y + 3)/3 = (z - 14)/4`, is ______.
