Advertisements
Advertisements
प्रश्न
M and N are two points on the X axis and Y axis respectively. P (3, 2) divides the line segment MN in the ratio 2 : 3.
Find:
(i) the coordinates of M and N
(ii) slope of the line MN.
उत्तर
Let coordinates of M is (a, 0) and M is (0, b).
Point P divides MN in 2 : 3 ratio
`therefore 3 =(3a + 2 xx 0 )/ (3 + 2) " and " 2 =(3xx0+2xx b)/(3+2)`
3a = 15 and 10 = 2b
a = 5 and b = 5
(i) The coordinates of M is (5, 0) and N(0, 5)
(ii) Slope of the line MN `= (0-5)/(5-0) = -1 `
APPEARS IN
संबंधित प्रश्न
Find the ratio in which y-axis divides the line segment joining the points A(5, –6) and B(–1, –4). Also find the coordinates of the point of division.
If the points A (6, 1), B (8, 2), C(9, 4) and D(p, 3) are vertices of a parallelogram, taken in order, find the value of p
If the coordinates of the mid-points of the sides of a triangle are (1, 2) (0, –1) and (2, 1). Find the coordinates of its vertices.
Find the coordinates of the points which divide the line segment joining A (−2, 2) and B (2, 8) into four equal parts.
Three vertices of a parallelogram are (a+b, a-b), (2a+b, 2a-b), (a-b, a+b). Find the fourth vertex.
If two adjacent vertices of a parallelogram are (3, 2) and (−1, 0) and the diagonals intersect at (2, −5), then find the coordinates of the other two vertices.
If 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:
Find the ratio in which the line x = -2 divides the line segment joining (-6, -1) and (1, 6). Find the coordinates of the point of intersection.
Point P(– 4, 6) divides point A(– 6, 10) and B(m, n) in the ratio 2:1, then find the coordinates of point B
The perpendicular bisector of the line segment joining the points A(1, 5) and B(4, 6) cuts the y-axis at ______.
