Advertisements
Advertisements
Question
The equation of the straight line passing through the point (3, 2) and perpendicular to the line y = x is ______.
Options
x – y = 5
x + y = 5
x + y = 1
x – y = 1
Advertisements
Solution
The equation of the straight line passing through the point (3, 2) and perpendicular to the line y = x is x + y = 5.
Explanation:
Equation of line ‘l’ is given by y – y1 = m(x – x1).
Since l passing through the point P(3, 2).
∴ y – 2 = m(x – 3)
⇒ y = mx + 2 – 3m .....(i)
Since it is given that lines y = x
And ‘l’ are perpendicular to each other
∴ `"m" xx1`= –1 .....`[because "m"_1 xx "m"_2 = - 1]`
m = –1
Put m = – 1 in eqn. (i), we get
y = –x + 2 – 3(–1)
y = –x + 5
x + y = 5
APPEARS IN
RELATED QUESTIONS
Draw a quadrilateral in the Cartesian plane, whose vertices are (–4, 5), (0, 7), (5, –5) and (–4, –2). Also, find its area.
Find a point on the x-axis, which is equidistant from the points (7, 6) and (3, 4).
Find the slope of the line, which makes an angle of 30° with the positive direction of y-axis measured anticlockwise.
Find the angle between the x-axis and the line joining the points (3, –1) and (4, –2).
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.
Consider the given 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 equation of a line drawn perpendicular to the line `x/4 + y/6 = 1`through the point, where it meets the y-axis.
Find the slope of the lines which make the following angle with the positive direction of x-axis:
\[- \frac{\pi}{4}\]
Find the slope of the lines which make the following angle with the positive direction of x-axis: \[\frac{\pi}{3}\]
Find the slope of a line passing through the following point:
(−3, 2) and (1, 4)
State whether the two lines in each of the following is parallel, perpendicular or neither.
Through (6, 3) and (1, 1); through (−2, 5) and (2, −5)
Find the slope of a line (i) which bisects the first quadrant angle (ii) which makes an angle of 30° with the positive direction of y-axis measured anticlockwise.
What can be said regarding a line if its slope is positive ?
What can be said regarding a line if its slope is negative?
Show that the line joining (2, −3) and (−5, 1) is parallel to the line joining (7, −1) and (0, 3).
Show that the line joining (2, −5) and (−2, 5) is perpendicular to the line joining (6, 3) and (1, 1).
The slope of a line is double of the slope of another line. If tangents of the angle between them is \[\frac{1}{3}\],find the slopes of the other line.
Find the value of x for which the points (x, −1), (2, 1) and (4, 5) are collinear.
A quadrilateral has vertices (4, 1), (1, 7), (−6, 0) and (−1, −9). Show that the mid-points of the sides of this quadrilateral form a parallelogram.
Find the equation of a straight line with slope 2 and y-intercept 3 .
Find the equations of the straight lines which cut off an intercept 5 from the y-axis and are equally inclined to the axes.
Find the angles between the following pair of straight lines:
3x − y + 5 = 0 and x − 3y + 1 = 0
Find the tangent of the angle between the lines which have intercepts 3, 4 and 1, 8 on the axes respectively.
Show that the line a2x + ay + 1 = 0 is perpendicular to the line x − ay = 1 for all non-zero real values of a.
The acute angle between the medians drawn from the acute angles of a right angled isosceles triangle is
The coordinates of the foot of the perpendicular from the point (2, 3) on the line x + y − 11 = 0 are
The reflection of the point (4, – 13) about the line 5x + y + 6 = 0 is ______.
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.
If p is the length of perpendicular from the origin on the line `x/a + y/b` = 1 and a2, p2, b2 are in A.P, then show that a4 + b4 = 0.
Equation of the line passing through (1, 2) and parallel to the line y = 3x – 1 is ______.
The points A(– 2, 1), B(0, 5), C(– 1, 2) are collinear.
The vertex of an equilateral triangle is (2, 3) and the equation of the opposite side is x + y = 2. Then the other two sides are y – 3 = `(2 +- sqrt(3)) (x - 2)`.
The line `x/a + y/b` = 1 moves in such a way that `1/a^2 + 1/b^2 = 1/c^2`, where c is a constant. The locus of the foot of the perpendicular from the origin on the given line is x2 + y2 = c2.
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 ______.
The three straight lines ax + by = c, bx + cy = a and cx + ay = b are collinear, if ______.
