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
Advertisements
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
If A(–2, 1), B(a, 0), C(4, b) and D(1, 2) are the vertices of a parallelogram ABCD, find the values of a and b. Hence find the lengths of its sides
The base PQ of two equilateral triangles PQR and PQR' with side 2a lies along y-axis such that the mid-point of PQ is at the origin. Find the coordinates of the vertices R and R' of the triangles.
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.
Determine the ratio in which the point (-6, a) divides the join of A (-3, 1) and B (-8, 9). Also, find the value of a.
Find the coordinates of the midpoints of the line segment joining
P(-11,-8) and Q(8,-2)
Find the ratio in which the point P(m, 6) divides the join of A(-4, 3) and B(2, 8) Also, find the value of m.
Find the ratio in which the pint (-3, k) divide the join of A(-5, -4) and B(-2, 3),Also, find the value of k.
Point P(x, 4) lies on the line segment joining the points A(−5, 8) and B(4, −10). Find the ratio in which point P divides the line segment AB. Also find the value of x.
If A(−3, 5), B(−2, −7), C(1, −8) and D(6, 3) are the vertices of a quadrilateral ABCD, find its area.
\[A\left( 6, 1 \right) , B(8, 2) \text{ and } C(9, 4)\] are three vertices of a parallelogram ABCD . If E is the mid-point of DC , find the area of \[∆\] ADE.
If \[D\left( - \frac{1}{5}, \frac{5}{2} \right), E(7, 3) \text{ and } F\left( \frac{7}{2}, \frac{7}{2} \right)\] are the mid-points of sides of \[∆ ABC\] , find the area of \[∆ ABC\] .
If the distance between points (x, 0) and (0, 3) is 5, what are the values of x?
The perimeter of the triangle formed by the points (0, 0), (0, 1) and (0, 1) is
The ratio in which the x-axis divides the segment joining (3, 6) and (12, −3) is
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 =
If the points P (x, y) is equidistant from A (5, 1) and B (−1, 5), then
If P(2, 4), Q(0, 3), R(3, 6) and S(5, y) are the vertices of a parallelogram PQRS, then the value of y is
The perpendicular distance of the point P(3, 4) from the y-axis is ______.
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 (3, 5) from x-axis (in units) is ______.
