Advertisements
Advertisements
प्रश्न
Find the coordinates of a point P on the line segment joining A(1, 2) and B(6, 7) in such a way that AP = `2/5` AB
उत्तर
Let the point A(1, 2) and B(6, 7)
AP = `2/5` AB
`"AP"/"PB" = 2/5`
∴ AP = 2, PB = 5 – 2 = 3
A line divides internally in the ratio m : n
The point P = `(("m"x_2 + "n"x_1)/("m" + "n"), ("m"y_2 + "n"y_1)/("m" + "n"))`
m = 2, n = 3, x1 = 1, x2 = 6, y1 = 2, y2 = 7
The point P is (3, 4)
= `((2 xx 6 + 3 xx 1)/(2 + 3), (2 xx 7 + 3 xx 2)/(2 + 3))`
= `((12 + 3)/5, (14 + 6)/5)`
= `(15/5, 20/5)`
= (3, 4)
APPEARS IN
संबंधित प्रश्न
Find the coordinates of the point which divides the line segment joining the points A(4, −3) and B(9, 7) in the ratio 3 : 2
In what ratio does the point P(2, −5) divide the line segment joining A(−3, 5) and B(4, −9)
Find the coordinates of the points of trisection of the line segment joining the points A(−5, 6) and B(4, −3)
The line segment joining A(6, 3) and B(−1, −4) is doubled in length by adding half of AB to each end. Find the coordinates of the new end points.
A line segment AB is increased along its length by 25% by producing it to C on the side of B. If A and B have the coordinates (−2, −3) and (2, 1) respectively, then find the coordinates of C.
If the coordinates of the mid-points of the sides AB, BC and CA of a triangle are (3, 4), (1, 1) and (2, −3) respectively, then the vertices A and B of the triangle are
