Advertisements
Advertisements
Question
In what ratio does the point P(2,5) divide the join of A (8,2) and B(-6, 9)?
Advertisements
Solution
Let the point P (2,5) divide AB in the ratio k : 1
Then, by section formula, the coordinates of P are
` x= (-6k+8)/(k+1) , y = (9k+2)/(k+1)`
It is given that the coordinates of P are ( 2,5).
`⇒ 2= (-6k +8) /(k+1) , 5 =(9k +2) /(k+1) `
⇒ 2k + 2 = -6k +8 , 5k +5 = 9k +2
⇒ 2k + 6k = 8 -2 , 5-2=9k-5k
⇒ 8k = 6, 4k =3
⇒` k = 6/8, k = 3/4 `
`⇒ k = 3/4 ` in each case..
Therefore, the point P (2,5) divides AB in the ratio3:4
APPEARS IN
RELATED QUESTIONS
Three consecutive vertices of a parallelogram are (-2,-1), (1, 0) and (4, 3). Find the fourth vertex.
The points A(2, 0), B(9, 1) C(11, 6) and D(4, 4) are the vertices of a quadrilateral ABCD. Determine whether ABCD is a rhombus or not.
The line joining the points (2, 1) and (5, −8) is trisected at the points P and Q. If point P lies on the line 2x − y + k = 0. Find the value of k.
Show that the following points are the vertices of a rectangle.
A (2, -2), B(14,10), C(11,13) and D(-1,1)
Find the area of the triangle formed by joining the midpoints of the sides of the triangle whose vertices are A(2,1) B(4,3) and C(2,5)
If `P(a/2,4)`is the mid-point of the line-segment joining the points A (−6, 5) and B(−2, 3), then the value of a is
Show that `square` ABCD formed by the vertices A(-4,-7), B(-1,2), C(8,5) and D(5,-4) is a rhombus.
The measure of the angle between the coordinate axes is
Two points having same abscissae but different ordinate lie on
The area of the triangle formed by the points A(2,0) B(6,0) and C(4,6) is
Show that ΔABC, where A(–2, 0), B(2, 0), C(0, 2) and ΔPQR where P(–4, 0), Q(4, 0), R(0, 2) are similar triangles.
If A(−3, 5), B(−2, −7), C(1, −8) and D(6, 3) are the vertices of a quadrilateral ABCD, find its area.
Find the area of a parallelogram ABCD if three of its vertices are A(2, 4), B(2 + \[\sqrt{3}\] , 5) and C(2, 6).
Write the perimeter of the triangle formed by the points O (0, 0), A (a, 0) and B (0, b).
If the points (k, 2k), (3k, 3k) and (3, 1) are collinear, then k
Find the point on the y-axis which is equidistant from the points (5, −2) and (−3, 2).
If the sum of X-coordinates of the vertices of a triangle is 12 and the sum of Y-coordinates is 9, then the coordinates of centroid are ______
Point (–3, 5) lies in the ______.
The coordinates of a point whose ordinate is `-1/2` and abscissa is 1 are `-1/2, 1`.
(–1, 7) is a point in the II quadrant.
