Advertisements
Advertisements
Question
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
Solution
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
RELATED QUESTIONS
Prove that the points (3, 0), (6, 4) and (-1, 3) are the vertices of a right-angled isosceles triangle.
Show that the points (−3, 2), (−5,−5), (2, −3) and (4, 4) are the vertices of a rhombus. Find the area of this rhombus.
Prove that the points A(-4,-1), B(-2, 4), C(4, 0) and D(2, 3) are the vertices of a rectangle.
The measure of the angle between the coordinate axes is
A point whose abscissa is −3 and ordinate 2 lies in
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 the points P, Q(x, 7), R, S(6, y) in this order divide the line segment joining A(2, p) and B(7, 10) in 5 equal parts, find x, y and p.
Find the value of a so that the point (3, a) lies on the line represented by 2x − 3y + 5 = 0
A line segment is of length 10 units. If the coordinates of its one end are (2, −3) and the abscissa of the other end is 10, then its ordinate is
If A (2, 2), B (−4, −4) and C (5, −8) are the vertices of a triangle, than the length of the median through vertex C is
The ratio in which (4, 5) divides the join of (2, 3) and (7, 8) is
If Points (1, 2) (−5, 6) and (a, −2) are collinear, then a =
Which of the points P(-1, 1), Q(3, - 4), R(1, -1), S (-2, -3), T(-4, 4) lie in the fourth quadrant?
Write the equations of the x-axis and y-axis.
Find the point on the y-axis which is equidistant from the points (5, −2) and (−3, 2).
The points (–5, 2) and (2, –5) lie in the ______.
If the coordinates of the two points are P(–2, 3) and Q(–3, 5), then (abscissa of P) – (abscissa of Q) is ______.
The perpendicular distance of the point P(3, 4) from the y-axis is ______.
(–1, 7) is a point in the II quadrant.
The distance of the point (–4, 3) from y-axis is ______.
