हिंदी

Find the Slope of a Line Passing Through the Following Point: (−3, 2) and (1, 4)

Advertisements
Advertisements

प्रश्न

Find the slope of a line passing through the following point:

 (−3, 2) and (1, 4)

संक्षेप में उत्तर
Advertisements

उत्तर

(−3, 2) and (1, 4)

Let m be the slope of the given line.

\[\therefore m = \frac{y_2 - y_1}{x_2 - x_1}\]

\[ \Rightarrow m = \frac{4 - 2}{1 + 3} = \frac{2}{4} = \frac{1}{2}\]

Hence, the slope of the line passing through the points (−3, 2) and (1, 4) is \[\frac{1}{2}\].

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 23: The straight lines - Exercise 23.1 [पृष्ठ १३]

APPEARS IN

आर.डी. शर्मा Mathematics [English] Class 11
अध्याय 23 The straight lines
Exercise 23.1 | Q 2.1 | पृष्ठ १३

वीडियो ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्न

Draw a quadrilateral in the Cartesian plane, whose vertices are (–4, 5), (0, 7), (5, –5) and (–4, –2). Also, find its area.


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.


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


Find the values of k for which the line (k–3) x – (4 – k2) y + k2 –7k + 6 = 0 is 

  1. Parallel to the x-axis,
  2. Parallel to the y-axis,
  3. Passing through the origin.

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 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.


Using the method of slope, show that the following points are collinear A (16, − 18), B (3, −6), C (−10, 6) .


What is the value of y so that the line through (3, y)  and (2, 7) is parallel to the line through (−1, 4) and (0, 6)?


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).


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.


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 the X-axis and the line joining the points (3, −1) and (4, −2).


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


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


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 the perpendicular to the line segment joining (4, 3) and (−1, 1) if it cuts off an intercept −3 from y-axis.


Find the equations of the straight lines which cut off an intercept 5 from the y-axis and are equally inclined to the axes.


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).


If the image of the point (2, 1) with respect to a line mirror is (5, 2), find the equation of the mirror.


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.


The angle between the lines 2x − y + 3 = 0 and x + 2y + 3 = 0 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 reflection of the point (4, −13) about the line 5x + y + 6 = 0 is  


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 ______.


If x + y = k is normal to y2 = 12x, then k is ______.


The line passing through (– 2, 0) and (1, 3) makes an angle of ______ with X-axis.


The coordinates of the foot of the perpendicular from the point (2, 3) on the line x + y – 11 = 0 are ______.


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


The equation of the straight line passing through the point (3, 2) and perpendicular to the line y = x is ______.


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


Equations of the lines through the point (3, 2) and making an angle of 45° with the line x – 2y = 3 are ______.


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)`

The equation of the line through the intersection of the lines 2x – 3y = 0 and 4x – 5y = 2 and

Column C1 Column C2
(a) Through the point (2, 1) is (i) 2x – y = 4
(b) Perpendicular to the line (ii) x + y – 5
= 0 x + 2y + 1 = 0 is
(ii) x + y – 5 = 0
(c) Parallel to the line (iii) x – y –1 = 0
3x – 4y + 5 = 0 is
(iii) x – y –1 = 0
(d) Equally inclined to the axes is (iv) 3x – 4y – 1 = 0

A ray of light coming from the point (1, 2) is reflected at a point A on the x-axis and then passes through the point (5, 3). The co-ordinates of the point A is ______.


If the line joining two points A (2, 0) and B (3, 1) is rotated about A in anticlockwise direction through an angle of 15°, then the equation of the line in new position is ______.


The lines whose vector equations are `r = 2hati - 3hatj + 7hatk + lambda (2hati + phatj + 5hatk) and r = hati - 2hatj + 3hatk + µ(3hati + phatj + phatk)` are perpendicular for all values of λ and µ if p =


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×