Advertisements
Advertisements
प्रश्न
Points P, Q, R and S divide the line segment joining the points A(1,2) and B(6,7) in five equal parts. Find the coordinates of the points P,Q and R
उत्तर
Since, the points P, Q, R and S divide the line segment joining the points
A (1,2) and B ( 6,7) in five equal parts, so
AP = PQ = QR = R = SB
Here, point P divides AB in the ratio of 1 : 4 internally So using section formula, we get
`"Coordinates of P "= ((1xx(6) +4xx(1))/(1+4) = (1 xx(7) +4xx(2))/(1+4))`
`= ((6+4)/5 , (7+8)/5) = (2,3)`
The point Q divides AB in the ratio of 2 : 3 internally. So using section formula, we get
`"Coordinates of Q " =((2 xx(6) +3 xx(1))/(2+3) = (2xx(7) +3xx(2))/(2+3))`
`= ((12+3)/5 , (14+6)/5) = (3,4)`
The point R divides AB in the ratio of 3 : 2 internally So using section formula, we get
`"Coordinates of R " = ((3 xx(6) +2 xx(1))/(3+2) = (3xx(7) +2 xx(2))/(3+2))`
`= ((18+2)/5 = (21+4)/5) = (4,5)`
Hence, the coordinates of the points P, Q and R are (2,3) , (3,4) and (4,5) respectively
संबंधित प्रश्न
In what ratio is the line segment joining (-3, -1) and (-8, -9) divided at the point (-5, -21/5)?
Points P, Q, and R in that order are dividing line segment joining A (1,6) and B(5, -2) in four equal parts. Find the coordinates of P, Q and R.
If the point `P (1/2,y)` lies on the line segment joining the points A(3, -5) and B(-7, 9) then find the ratio in which P divides AB. Also, find the value of y.
If the point A(0,2) is equidistant from the points B(3,p) and C(p, 5), find p.
If the point P(k-1, 2) is equidistant from the points A(3,k) and B(k,5), find the value of k.
If the points A(4,3) and B( x,5) lie on the circle with center O(2,3 ) find the value of x .
If the points A (2,3), B (4,k ) and C (6,-3) are collinear, find the value of k.
ΔXYZ ∼ ΔPYR; In ΔXYZ, ∠Y = 60o, XY = 4.5 cm, YZ = 5.1 cm and XYPY =` 4/7` Construct ΔXYZ and ΔPYR.
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 value of k if points A(k, 3), B(6, −2) and C(−3, 4) are collinear.
Write the distance between the points A (10 cos θ, 0) and B (0, 10 sin θ).
What is the distance between the points (5 sin 60°, 0) and (0, 5 sin 30°)?
If (−1, 2), (2, −1) and (3, 1) are any three vertices of a parallelogram, then
If the points P (x, y) is equidistant from A (5, 1) and B (−1, 5), then
The coordinates of a point on x-axis which lies on the perpendicular bisector of the line segment joining the points (7, 6) and (−3, 4) 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
What is the nature of the line which includes the points (-5, 5), (6, 5), (-3, 5), (0, 5)?
The line segment joining the points (3, -1) and (-6, 5) is trisected. The coordinates of point of trisection are ______.
If the coordinates of the two points are P(–2, 3) and Q(–3, 5), then (abscissa of P) – (abscissa of Q) is ______.
The distance of the point (–4, 3) from y-axis is ______.
