मराठी
महाराष्ट्र राज्य शिक्षण मंडळएचएससी विज्ञान (सामान्य) इयत्ता ११ वी

Answer the following question: Find the value of k the point P(1, k) lies on the line passing through the points A(2, 2) and B(3, 3) - Mathematics and Statistics

Advertisements
Advertisements

प्रश्न

Answer the following question:

Find the value of k the point P(1, k) lies on the line passing through the points A(2, 2) and B(3, 3)

बेरीज

उत्तर

Since P(1, k) lies on the line passing through the points A(2, 2) and B(3, 3), the points P, A, B are collinear.

∴ slope of AP = slope of AB

∴ `("k" - 2)/(1 - 2) = (3 - 2)/(3 - 2)`

∴ `("k" - 2)/(-1) = 1/1` = 1

∴ k – 2 = –1

∴ k = 1

shaalaa.com
Straight Lines
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 5: Straight Line - Miscellaneous Exercise 5 [पृष्ठ १२४]

APPEARS IN

बालभारती Mathematics and Statistics 1 (Arts and Science) [English] 11 Standard Maharashtra State Board
पाठ 5 Straight Line
Miscellaneous Exercise 5 | Q II. (1) (c) | पृष्ठ १२४

संबंधित प्रश्‍न

Find the slope of the line whose inclination is 30°


A line makes intercepts 3 and 3 on the co-ordinate axes. Find the inclination of the line.


Without using Pythagoras theorem show that points A(4, 4), B(3, 5) and C(−1, −1) are the vertices of a right angled triangle.


Find the slope of the line which makes angle of 45° with the positive direction of the Y-axis measured anticlockwise


Find the value of k for which points P(k, −1), Q(2, 1) and R(4, 5) are collinear.


If points A(h, 0), B(0, k) and C(a, b) lie on a line then show that `"a"/"h" + "b"/"k"` = 1


Select the correct option from the given alternatives:

If A is (5, −3) and B is a point on the x-axis such that the slope of line AB is −2 then B ≡


Select the correct option from the given alternatives:

If kx + 2y − 1 = 0 and 6x − 4y + 2 = 0 are identical lines, then determine k


Answer the following question:

Find the value of k if the slope of the line passing through the points P(3, 4), Q(5, k) is 9


Answer the following question:

Find the value of k the points A(1, 3), B(4, 1), C(3, k) are collinear


Find the equation of the lines passing through the point (1,1) with slope 3


If P(r, c) is midpoint of a line segment between the axes then show that `x/"r" + y/"c"` = 2


Find the equation of the line passing through the point (1, 5) and also divides the co-ordinate axes in the ratio 3:10


Population of a city in the years 2005 and 2010 are 1,35,000 and 1,45,000 respectively. Find the approximate population in the year 2015. (assuming that the growth of population is constant)


Find the equation of the straight lines passing through (8, 3) and having intercepts whose sum is 1


Show that the points (1, 3), (2, 1) and `(1/2, 4)` are collinear, by using concept of slope 


Show that the points (1, 3), (2, 1) and `(1/2, 4)` are collinear, by using a straight line


A 150 m long train is moving with constant velocity of 12.5 m/s. Find time taken to cross a pole


A spring was hung from a hook in the ceiling. A number of different weights were attached to the spring to make it stretch, and the total length of the spring was measured each time is shown in the following table

Weight (kg) 2 4 5 8
Length (cm) 3 4 4.5 6

Find the equation relating the length of the spring to the weight on it


A family is using Liquefied petroleum gas (LPG) of weight 14.2 kg for consumption. (Full weight 29.5kg includes the empty cylinders tare weight of 15.3kg.). If it is used with constant rate then it lasts for 24 days. Then the new cylinder is replaced. Find the equation relating the quantity of gas in the cylinder to the days


In a shopping mall there is a hall of cuboid shape with dimension 800 × 800 × 720 units, which needs to be added the facility of an escalator in the path as shown by the dotted line in the figure. Find the heights at which the escalator changes its direction


In a shopping mall there is a hall of cuboid shape with dimension 800 × 800 × 720 units, which needs to be added the facility of an escalator in the path as shown by the dotted line in the figure. Find the slopes of the escalator at the turning points


Choose the correct alternative:
Straight line joining the points (2, 3) and (−1, 4) passes through the point (α, β) if


Choose the correct alternative:
The y-intercept of the straight line passing through (1, 3) and perpendicular to 2x − 3y + 1 = 0 is


If one of the lines given by kx2 + 2xy – 3y2 = 0 is perpendicular to the line 3x + 5y+ 1 = 0, then the value of k is ______.


A point on the straight line, 3x + 5y = 15 which is equidistant from the coordinate, axes will lie only in ______.


The locus of the point of intersection of the lines xcosα + ysinα = α and xsinα – ycosα = b(where α is a variable) is ______.


The coordinates of vertices of base BC of an isosceles triangle ABC are given by B(1, 3) and C(–2, 7) which of the following points can be the possible coordinates of the vertex A?


The locus of the midpoint of the portion intercept between the axes by the line xcosa + ysina = P where P is a constant is ______.


If planes x – cy – bz = 0, cx – y + az = 0 and bx + ay – z = 0 pass through a straight line then a2 + b2 + c2 = ______.


Find the transformed equation of the straight line 2x – 3y + 5 = 0, when the origin is shifted to the point (3, –1) after translation of axes.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×