Advertisements
Advertisements
प्रश्न
The point R divides the line segment AB, where A(−4, 0) and B(0, 6) such that AR=34AB.">AR = `3/4`AB. Find the coordinates of R.
Advertisements
उत्तर
We have given that R divides the line segment AB
AR+ RB = AB
`3/4`AB + RB = AB
⇒ RB = `"AB"/4`
⇒ AR : RB = 3 : 1
Using section formula:
`x = ((m_1x_2 + m_2x_1)/( m_1 + m_2)), y = ((m_1y_2 + m_2y_1)/(m_1 + m_2))`
m1 = 3, m2 = 1
x1 = - 4, y1 = 0
x2 = 0, y2 = 6
Plugging values in the formula we get
x = `( 3 xx 0 + 1 xx (- 4))/( 3 + 1), y = ( 3 xx 6 + 1 xx 0)/( 3 + 1)`
x = `(- 4)/4, y = 18/4`
⇒ x = - 1, y = `9/2`
Therefore, the coordinates of R `(-1,9/2)`
संबंधित प्रश्न
Which point on the y-axis is equidistant from (2, 3) and (−4, 1)?
If two opposite vertices of a square are (5, 4) and (1, −6), find the coordinates of its remaining two vertices.
A (3, 2) and B (−2, 1) are two vertices of a triangle ABC whose centroid G has the coordinates `(5/3,-1/3)`Find the coordinates of the third vertex C of the triangle.
If the points A(4,3) and B( x,5) lie on the circle with center O(2,3 ) find the value of x .
Find the value of k if points A(k, 3), B(6, −2) and C(−3, 4) are collinear.
If A (1, 2) B (4, 3) and C (6, 6) are the three vertices of a parallelogram ABCD, find the coordinates of fourth vertex D.
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 (–4, 3) from y-axis is ______.
Distance of the point (6, 5) from the y-axis is ______.
Ryan, from a very young age, was fascinated by the twinkling of stars and the vastness of space. He always dreamt of becoming an astronaut one day. So, he started to sketch his own rocket designs on the graph sheet. One such design is given below :
Based on the above, answer the following questions:
i. Find the mid-point of the segment joining F and G. (1)
ii. a. What is the distance between the points A and C? (2)
OR
b. Find the coordinates of the points which divides the line segment joining the points A and B in the ratio 1 : 3 internally. (2)
iii. What are the coordinates of the point D? (1)
