Advertisements
Advertisements
प्रश्न
Find the coordinates of a point P, which lies on the line segment joining the points A (−2, −2), and B (2, −4), such that `AP=3/7 AB`.
उत्तर
It is given that,`AP=3/7 AB`. where A, P and B are three points on line segment AB.
`rArr(AB)/(AP)=7/3`
`rArr(AB)/(AP)=-1=7/3-1`
`rArr(AB-AP)/(AP)=(7-3)/3`
`rArr (PB)/(AP)=4/3`
Thus, AP : PB = 3 : 4
It is given that, the coordinates of points A and B are (−2, −2) and (2, −4).
Using section formula,
Coordinates P are `((3xx2+4xx(-2))/(3+4),(3xx(-4)+4xx(-2))/(3+4))`
`=((6-8)/7,(-12-8)/7)=(-2/7,-20/7)`
Hence, the coordinates of point P are`(-2/7,-20/7)`
APPEARS IN
संबंधित प्रश्न
If A and B are (−2, −2) and (2, −4), respectively, find the coordinates of P such that `"AP" = 3/7 "AB"` and P lies on the line segment AB.
If the mid-point of the line joining (3, 4) and (k, 7) is (x, y) and 2x + 2y + 1 = 0 find the value of k.
The line segment joining the points M(5, 7) and N(–3, 2) is intersected by the y-axis at point L. Write down the abscissa of L. Hence, find the ratio in which L divides MN. Also, find the co-ordinates of L.
A (2, 5), B (–1, 2) and C (5, 8) are the co-ordinates of the vertices of the triangle ABC. Points P and Q lie on AB and AC respectively, such that : AP : PB = AQ : QC = 1 : 2.
- Calculate the co-ordinates of P and Q.
- Show that : `PQ = 1/3 BC`.
The line segment joining A(4, 7) and B(−6, −2) is intercepted by the y – axis at the point K. write down the abscissa of the point K. hence, find the ratio in which K divides AB. Also, find the co-ordinates of the point K.
A line segment joining A`(-1,5/3)` and B(a, 5) is divided in the ratio 1 : 3 at P, the point where the line segment AB intersects the y-axis.
- Calculate the value of ‘a’.
- Calculate the co-ordinates of ‘P’.
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.
Find the coordinate of a point P which divides the line segment joining :
D(-7, 9) and E( 15, -2) in the ratio 4:7.
Find the ratio in which the line x = O divides the join of ( -4, 7) and (3, 0).
Also, find the coordinates of the point of intersection.
Find the points of trisection of the segment joining A ( -3, 7) and B (3, -2).
