English

A line passes through (x1, y1) and (h, k). If slope of the line is m, show that k – y1 = m (h – x1). - Mathematics

Advertisements
Advertisements

Question

A line passes through (x1, y1) and (h, k). If slope of the line is m, show that k – y1 = m (h – x1).

Sum
Advertisements

Solution

The slope of the line passing through (x, y) and (h, k) is `(k - y_1)/(h - x_1)`

It is given that the slope of the line is m.

`("k" - "y"_1)/("h" - "x"_1) = "m"`

= k – y1 = m(h – x1)

Hence, k – y1 = m(h – x1)

shaalaa.com
  Is there an error in this question or solution?
Chapter 10: Straight Lines - Exercise 10.1 [Page 212]

APPEARS IN

NCERT Mathematics [English] Class 11
Chapter 10 Straight Lines
Exercise 10.1 | Q 12 | Page 212

Video TutorialsVIEW ALL [1]

RELATED QUESTIONS

The base of an equilateral triangle with side 2a lies along they y-axis such that the mid point of the base is at the origin. Find vertices of the triangle.


Find the distance between P (x1, y1) and Q (x2, y2) when :

  1. PQ is parallel to the y-axis,
  2. PQ is parallel to the x-axis

Find a point on the x-axis, which is equidistant from the points (7, 6) and (3, 4).


Find the slope of a line, which passes through the origin, and the mid-point of the line segment joining the points P (0, –4) and B (8, 0).


Find the value of x for which the points (x, –1), (2, 1) and (4, 5) are collinear.


Without using distance formula, show that points (–2, –1), (4, 0), (3, 3) and (–3, 2) are vertices of a parallelogram.


Find the angle between the x-axis and the line joining the points (3, –1) and (4, –2).


If three point (h, 0), (a, b) and (0, k) lie on a line, show that `q/h + b/k = 1`


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 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 equation of the lines through the point (3, 2) which make an angle of 45° with the line x –2y = 3.


Find the slope of the lines which make the following angle with the positive direction of x-axis: 

\[\frac{3\pi}{4}\]


If three points A (h, 0), P (a, b) and B (0, k) lie on a line, show that: \[\frac{a}{h} + \frac{b}{k} = 1\].


Find the equation of the strainght line intersecting y-axis at a distance of 2 units above the origin and making an angle of 30° with the positive direction of the x-axis.


Show that the perpendicular bisectors of the sides of a triangle are concurrent.


Find the equations of the altitudes of a ∆ ABC whose vertices are A (1, 4), B (−3, 2) and C (−5, −3).


The line through (h, 3) and (4, 1) intersects the line 7x − 9y − 19 = 0 at right angle. Find the value of h.


Find the image of the point (3, 8) with respect to the line x + 3y = 7 assuming the line to be a plane mirror.


Find the angles between the following pair of straight lines:

3x − y + 5 = 0 and x − 3y + 1 = 0


Find the angles between the following pair of straight lines:

x − 4y = 3 and 6x − y = 11


Find the angles between the following pair of straight lines:

(m2 − mn) y = (mn + n2) x + n3 and (mn + m2) y = (mn − n2) x + m3.


Prove that the points (2, −1), (0, 2), (2, 3) and (4, 0) are the coordinates of the vertices of a parallelogram and find the angle between its diagonals.


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 \[\left( \frac{a}{b} \right)\].


Find the tangent of the angle between the lines which have intercepts 3, 4 and 1, 8 on the axes respectively.


The equation of a line passing through the point (7, - 4) and perpendicular to the line passing through the points (2, 3) and (1 , - 2 ) is ______.


Find the equation to the straight line passing through the point of intersection of the lines 5x – 6y – 1 = 0 and 3x + 2y + 5 = 0 and perpendicular to the line 3x – 5y + 11 = 0.


If one diagonal of a square is along the line 8x – 15y = 0 and one of its vertex is at (1, 2), then find the equation of sides of the square passing through this vertex.


Find the equation of one of the sides of an isosceles right angled triangle whose hypotenuse is given by 3x + 4y = 4 and the opposite vertex of the hypotenuse is (2, 2).


Slope of a line which cuts off intercepts of equal lengths on the axes is ______.


Equation of the line passing through (1, 2) and parallel to the line y = 3x – 1 is ______.


The points (3, 4) and (2, – 6) are situated on the ______ of the line 3x – 4y – 8 = 0.


If the vertices of a triangle have integral coordinates, then the triangle can not be equilateral.


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)`

Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×