Advertisements
Advertisements
प्रश्न
In what ratio is the line segment joining the points (-2,-3) and (3, 7) divided by the y-axis? Also, find the coordinates of the point of division.
Advertisements
उत्तर
The ratio in which the y-axis divides two points `(x_1,y_1)` and (x_2,y_2) is λ : 1
The coordinates of the point dividing two points `(x_1,y_1)` and `(x_2, y_2)` in the ratio m:n is given as,
`(x,y) = (((lambdax_2+ x_1)/(lambda + 1))"," ((lambday_2 + y_1)/(lambda +1)))` where `lambda = m/n`
Here the two given points are A(-2,-3) and B(3,7).
Since the point is on the y-axis so, x coordinate is 0.
`(3lambda - 2)/1 = 0`
`=> lambda = 2/3`
Thus the given points are divided by the y-axis in the ratio 2:3
The coordinates of this point (x, y) can be found by using the earlier mentioned formula.
`(x,y) = (((2/3(3) + (-2))/(2/3 + 1))","((2/3(7) + (-3))/(2/3 + 1)))`
`(x,y) = ((((6 - 2(3))/3)/((2+3)/3)) "," (((14 - 3(3))/3)/((2+3)/3)))`
`(x,y) = ((0/5)","(5/5))`
(x,y) = (0,1)
Thus the co-ordinates of the point which divides the given points in the required ratio are (0,1)
APPEARS IN
संबंधित प्रश्न
How will you describe the position of a table lamp on your study table to another person?
On which axis do the following points lie?
S(0,5)
In what ratio is the line segment joining (-3, -1) and (-8, -9) divided at the point (-5, -21/5)?
If p(x , y) is point equidistant from the points A(6, -1) and B(2,3) A , show that x – y = 3
Show that the following points are the vertices of a square:
A (0,-2), B(3,1), C(0,4) and D(-3,1)
`"Find the ratio in which the poin "p (3/4 , 5/12) " divides the line segment joining the points "A (1/2,3/2) and B (2,-5).`
ABCD is rectangle formed by the points A(-1, -1), B(-1, 4), C(5, 4) and D(5, -1). If P,Q,R and S be the midpoints of AB, BC, CD and DA respectively, Show that PQRS is a rhombus.
If the point C(k,4) divides the join of A(2,6) and B(5,1) in the ratio 2:3 then find the value of k.
Find the centroid of ΔABC whose vertices are A(2,2) , B (-4,-4) and C (5,-8).
The distance of the point P (4, 3) from the origin is
If the vertices of a triangle are (1, −3), (4, p) and (−9, 7) and its area is 15 sq. units, find the value(s) of p.
If the points A(−1, −4), B(b, c) and C(5, −1) are collinear and 2b + c = 4, find the values of b and c.
If the points A(1, –2), B(2, 3) C(a, 2) and D(– 4, –3) form a parallelogram, find the value of a and height of the parallelogram taking AB as base.
Write the coordinates of the point dividing line segment joining points (2, 3) and (3, 4) internally in the ratio 1 : 5.
If the centroid of the triangle formed by points P (a, b), Q(b, c) and R (c, a) is at the origin, what is the value of a + b + c?
Find the coordinates of the point which is equidistant from the three vertices A (\[2x, 0) O (0, 0) \text{ and } B(0, 2y) of ∆\] AOB .
If the area of the triangle formed by the points (x, 2x), (−2, 6) and (3, 1) is 5 square units , then x =
If the centroid of a triangle is (1, 4) and two of its vertices are (4, −3) and (−9, 7), then the area of the triangle 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`.
Assertion (A): The ratio in which the line segment joining (2, -3) and (5, 6) internally divided by x-axis is 1:2.
Reason (R): as formula for the internal division is `((mx_2 + nx_1)/(m + n) , (my_2 + ny_1)/(m + n))`
