हिंदी

Find the equation of the line which satisfy the given condition: The vertices of ΔPQR are P (2, 1), Q (–2, 3) and R (4, 5). Find equation of the median through the vertex R. - Mathematics

Advertisements
Advertisements

प्रश्न

Find the equation of the line which satisfy the given condition:

The vertices of ΔPQR are P (2, 1), Q (–2, 3) and R (4, 5). Find equation of the median through the vertex R.

योग

उत्तर

It is given that the vertices of ΔPQR are P (2, 1), Q (–2, 3), and R (4, 5).

Let RL be the median through vertex R.

Accordingly, L is the mid-point of PQ.

By mid-point formula, the coordinates of point L are given by `((2 - 2)/2, (1 + 3)/2) = (0, 2)`

It is known that the equation of the line passing through points (x1, y1) and (x2, y2) is y - y1 = `(y_2 - y_1)/(x_2 - x_1) (x - x_1)`

Therefore, the equation of RL can be determined by substituting (x1, y1) = (4, 5) and (x2, y2) = 0

Hence, `y - 5 = (2 - 5)/(0 - 4) (x - 4)`

= `y - 5 = (-3)/(-4) (x - 4)`

= 4(y - 5) = 3(x - 4)

= 4y - 20 = 3x - 12

= 3x - 4y + 8 = 0

Thus, the required equation of the median through vertex R is 3x - 4y + 8 = 0

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 10: Straight Lines - Exercise 10.2 [पृष्ठ २२०]

APPEARS IN

एनसीईआरटी Mathematics [English] Class 11
अध्याय 10 Straight Lines
Exercise 10.2 | Q 9 | पृष्ठ २२०

वीडियो ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्न

Find the equation of the line which satisfy the given condition:

Write the equations for the x and y-axes.


Find the equation of the line which satisfy the given condition:

Passing through the point (–4, 3) with slope `1/2`.


Find the equation of the line which satisfy the given condition:

Intersects the 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.


Find the equation of the line which satisfy the given condition:

Passing through the points (–1, 1) and (2, –4).


Find the equation of the line which is at a perpendicular distance of 5 units from the origin and the angle made by the perpendicular with the positive x-axis is 30°


The vertices of ΔPQR are P (2, 1), Q (–2, 3) and R (4, 5). Find equation of the median through the vertex R.


Find the equation of the line passing through (–3, 5) and perpendicular to the line through the points (2, 5) and (–3, 6).


Find equation of the line through the point (0, 2) making an angle  `(2pi)/3` with the positive x-axis. Also, find the equation of line parallel to it and crossing the y-axis at a distance of 2 units below the origin.


The perpendicular from the origin to a line meets it at the point (– 2, 9), find the equation of the line.


By using the concept of equation of a line, prove that the three points (3, 0), (–2, –2) and (8, 2) are collinear.


Find the area of the triangle formed by the lines y – x = 0, x + y = 0 and x – k = 0.


Classify the following pair of line as coincident, parallel or intersecting:

x − y = 0 and 3x − 3y + 5 = 0]


Classify the following pair of line as coincident, parallel or intersecting:

3x + 2y − 4 = 0 and 6x + 4y − 8 = 0.


Prove that the lines \[\sqrt{3}x + y = 0, \sqrt{3}y + x = 0, \sqrt{3}x + y = 1 \text { and } \sqrt{3}y + x = 1\]  form a rhombus.


Prove that the lines 2x − 3y + 1 = 0, x + y = 3, 2x − 3y = 2  and x + y = 4 form a parallelogram.


Find the angle between the lines x = a and by + c = 0..


Find the equation of the line mid-way between the parallel lines 9x + 6y − 7 = 0 and 3x + 2y + 6 = 0.

 

Prove that the area of the parallelogram formed by the lines a1x + b1y + c1 = 0, a1x + b1yd1 = 0, a2x + b2y + c2 = 0, a2x + b2y + d2 = 0 is  \[\left| \frac{\left( d_1 - c_1 \right)\left( d_2 - c_2 \right)}{a_1 b_2 - a_2 b_1} \right|\] sq. units.
Deduce the condition for these lines to form a rhombus.

 


Prove that the area of the parallelogram formed by the lines 3x − 4y + a = 0, 3x − 4y + 3a = 0, 4x − 3y− a = 0 and 4x − 3y − 2a = 0 is \[\frac{2}{7} a^2\] sq. units..


Show that the diagonals of the parallelogram whose sides are lx + my + n = 0, lx + my + n' = 0, mx + ly + n = 0 and mx + ly + n' = 0 include an angle π/2.


Three vertices of a parallelogram taken in order are (−1, −6), (2, −5) and (7, 2). The fourth vertex is


Let ABC be a triangle with A(–3, 1) and ∠ACB = θ, 0 < θ < `π/2`. If the equation of the median through B is 2x + y – 3 = 0 and the equation of angle bisector of C is 7x – 4y – 1 = 0, then tan θ is equal to ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×