Advertisements
Advertisements
प्रश्न
The line segment joining the points A(3,−4) and B(1,2) is trisected at the points P(p,−2) and Q `(5/3,q)`. Find the values of p and q.
Advertisements
उत्तर
Let P and Q be the points of trisection of AB.
Then, P divides AB in the radio 1:2
So, the coordinates of P are
` x= ((mx_2 +nx_1))/((m+n)) , y = ((my_2+ny_1))/((m+n))`
` ⇒ x = ({ 1 xx 1+2xx(3)})/(1+2) , y = ({1 xx 2+2xx(-4)})/(1+2)`
` ⇒ x = (1+6)/3 , y (2-8)/3`
` ⇒ x = 7/3 , y -6/3`
` ⇒x =7/3 , y =-2`
Hence, the coordinates of P are `(7/3, -2)`
But, (p -2) are the coordinates of P.
so, p = `7/3`
Also, Q divides the line AB in the ratio 2:1
So, the coordinates of Q are
`x = ((mx_2 +mx_1))/((m+n)) , y = ((my_2+my_1))/((m+n))`
`⇒x = ((2xx1+1xx3))/((2+1)) , y = ({ 2xx2+1xx(-4)})/(2+1)`
`⇒ x = (2+3)/3 , y = (4-4)/3`
`⇒ x = 5/3 , y =0`
Hence, coordinates of Q are `(5/3, 0)`
But the given coordinates of Q are `(5/3,q)`
so, q = 0
Thus, `p=7/3 and q =0`
APPEARS IN
संबंधित प्रश्न
Let ABCD be a square of side 2a. Find the coordinates of the vertices of this square when A coincides with the origin and AB and AD are along OX and OY respectively.
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.
Three consecutive vertices of a parallelogram are (-2,-1), (1, 0) and (4, 3). Find the fourth vertex.
Find the co-ordinates of the point equidistant from three given points A(5,3), B(5, -5) and C(1,- 5).
In what ratio does y-axis divide the line segment joining the points (-4, 7) and (3, -7)?
If the points A (2,3), B (4,k ) and C (6,-3) are collinear, find the value of k.
Find the ratio in which the point (−3, k) divides the line-segment joining the points (−5, −4) and (−2, 3). Also find the value of k ?
Find the coordinates of the centre of the circle passing through the points P(6, –6), Q(3, –7) and R (3, 3).
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).
If the points A(−2, 1), B(a, b) and C(4, −1) ae collinear and a − b = 1, find the values of aand b.
The perimeter of the triangle formed by the points (0, 0), (0, 1) and (0, 1) is
f the coordinates of one end of a diameter of a circle are (2, 3) and the coordinates of its centre are (−2, 5), then the coordinates of the other end of the diameter are
If A(4, 9), B(2, 3) and C(6, 5) are the vertices of ∆ABC, then the length of median through C is
Find the point on the y-axis which is equidistant from the points (5, −2) and (−3, 2).
The line 3x + y – 9 = 0 divides the line joining the points (1, 3) and (2, 7) internally in the ratio ______.
Point P(– 4, 2) lies on the line segment joining the points A(– 4, 6) and B(– 4, – 6).
If y-coordinate of a point is zero, then this point always lies ______.
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?
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`.
The distance of the point (–4, 3) from y-axis is ______.
