The Point R Divides the Line Segment Ab, Where A(−4, 0) and B(0, 6) Such that Ar = 3/4ab. Find the Coordinates Of R. - Mathematics

Advertisements
Advertisements
Sum

The point R divides the line segment AB, where A(−4, 0) and B(0, 6) such that AR=34AB.">AR = `3/4`AB. Find the coordinates of R.

Advertisements

Solution

We have given that R divides the line segment AB
AR+ RB = AB
`3/4`AB + RB = AB

⇒ RB = `"AB"/4`

⇒ AR : RB = 3 : 1
Using section formula:

`x = ((m_1x_2 + m_2x_1)/( m_1 + m_2)),  y = ((m_1y_2 + m_2y_1)/(m_1 + m_2))`

m1 = 3, m2 = 1
x1 = - 4, y1 = 0
x2 = 0, y2 = 6

Plugging values in the formula we get
x = `( 3 xx 0 + 1 xx (- 4))/( 3 + 1), y = ( 3 xx 6 + 1 xx 0)/( 3 + 1)`

x = `(- 4)/4, y = 18/4`
⇒ x = - 1, y = `9/2`
Therefore, the coordinates of R `(-1,9/2)`

  Is there an error in this question or solution?
2018-2019 (March) 30/4/3

Video TutorialsVIEW ALL [2]

RELATED QUESTIONS

On which axis do the following points lie?

R(−4,0)


If two opposite vertices of a square are (5, 4) and (1, −6), find the coordinates of its remaining two vertices.


In Fig. 14.36, a right triangle BOA is given C is the mid-point of the hypotenuse AB. Show that it is equidistant from the vertices O, A  and B. 

    

We have a right angled triangle,`triangle BOA`  right angled at O. Co-ordinates are B (0,2b); A (2a0) and C (0, 0).

 

 

 


Find the coordinates of the circumcentre of the triangle whose vertices are (3, 0), (-1, -6) and (4, -1). Also, find its circumradius.


A (3, 2) and B (−2, 1)  are two vertices of a triangle ABC whose centroid G has the coordinates `(5/3,-1/3)`Find the coordinates of the third vertex C of the triangle.


Prove that the points (3, 0), (4, 5), (-1, 4) and (-2, -1), taken in order, form a rhombus.
Also, find its area.


Prove that the points (3, -2), (4, 0), (6, -3) and (5, -5) are the vertices of a parallelogram.


Find the points on the x-axis, each of which is at a distance of 10 units from the point A(11, –8).


Show that the points A(2,1), B(5,2), C(6,4) and D(3,3) are the angular points of a parallelogram. Is this figure a rectangle?


ABCD is rectangle formed by the points A(-1, -1), B(-1, 4), C(5, 4) and D(5, -1). If P,Q,R and S be the midpoints of AB, BC, CD and DA respectively, Show that PQRS is a rhombus.


Prove that the diagonals of a rectangle ABCD with vertices A(2,-1), B(5,-1) C(5,6) and D(2,6) are equal and bisect each other


Find the point on x-axis which is equidistant from points A(-1,0) and B(5,0)


Find the value of a, so that the point ( 3,a ) lies on the line represented by 2x - 3y =5 .


 If the points  A (2,3),  B (4,k ) and C (6,-3) are collinear, find the value of k.


Find the coordinates of the circumcentre of a triangle whose vertices are (–3, 1), (0, –2) and (1, 3).


Find the coordinates of circumcentre and radius of circumcircle of ∆ABC if A(7, 1), B(3, 5) and C(2, 0) are given.


Find the possible pairs of coordinates of the fourth vertex D of the parallelogram, if three of its vertices are A(5, 6), B(1, –2) and C(3, –2).


The co-ordinates of point A and B are 4 and -8 respectively. Find d(A, B).


ΔXYZ ∼ ΔPYR; In ΔXYZ, ∠Y = 60o, XY = 4.5 cm, YZ = 5.1 cm and XYPY =` 4/7` Construct ΔXYZ and ΔPYR.


Mark the correct alternative in each of the following:
The point of intersect of the coordinate axes is


The measure of the angle between the coordinate axes is


A point whose abscissa and ordinate are 2 and −5 respectively, lies in


Points (−4, 0) and (7, 0) lie


Write the condition of collinearity of points (x1, y1), (x2, y2) and (x3, y3).

 

The line segment joining points (−3, −4), and (1, −2) is divided by y-axis in the ratio


If the centroid of the triangle formed by the points (a, b), (b, c) and (c, a) is at the origin, then a3 b3 + c3 =


The distance of the point (4, 7) from the x-axis is


If P is a point on x-axis such that its distance from the origin is 3 units, then the coordinates of a point on OY such that OP = OQ, are


The coordinates of the point P dividing the line segment joining the points A (1, 3) and B(4, 6) in the ratio 2 : 1 are


What is the form of coordinates of a point on the X-axis?


Any point on the line y = x is of the form ______.


In which quadrant does the point ( - 4, - 3) lie?


What is the nature of the line which includes the points ( -5, 5), (6, 5), (- 3, 5), (0, 5)?


Which of the points P ( -1, 1), Q (3, - 4), R(1, -1), S ( -2, - 3), T (- 4, 4) lie in the fourth quadrant?


In the above figure, seg PA, seg QB and RC are perpendicular to seg AC. From the information given in the figure, prove that: `1/x + 1/y = 1/z`


Find the point on the y-axis which is equidistant from the points (5, −2) and (−3, 2).


If segment AB is parallel Y-axis and coordinates of A are (1, 3), then the coordinates of B are ______


If point P is midpoint of segment joining point A(– 4, 2) and point B(6, 2), then the coordinates of P are ______


Write the X-coordinate and Y-coordinate of point P(– 5, 4)


What are the coordinates of origin?


Abscissa of all the points on the x-axis is ______.


If y-coordinate of a point is zero, then this point always lies ______.


If the perpendicular distance of a point P from the x-axis is 5 units and the foot of the perpendicular lies on the negative direction of x-axis, then the point P has ______.


Which of the points P(0, 3), Q(1, 0), R(0, – 1), S(–5, 0), T(1, 2) do not lie on the x-axis?


The perpendicular distance of the point P (3, 4) from the y-axis is ______.


(–1, 7) is a point in the II quadrant


Seg AB is parallel to X-axis and coordinates of the point A are (1, 3), then the coordinates of the point B can be ______.


If the coordinate of point A on the number line is –1 and that of point B is 6, then find d(A, B).


If the points P(1, 2), Q(0, 0) and R(x, y) are collinear, then find the relation between x and y.

Given points are P(1, 2), Q(0, 0) and R(x, y).

The given points are collinear, so the area of the triangle formed by them is `square`.

∴ `1/2 |x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2)| = square`

`1/2 |1(square) + 0(square) + x(square)| = square`

`square + square + square` = 0

`square + square` = 0

`square = square`

Hence, the relation between x and y is `square`.


Co-ordinates of origin are ______.


Share
Notifications



      Forgot password?
Use app×