Advertisements
Advertisements
प्रश्न
If the mid-point of the segment joining A (x, y + 1) and B (x + 1, y + 2) is C \[\left( \frac{3}{2}, \frac{5}{2} \right)\] , find x, y.
Advertisements
उत्तर
It is given that mid-point of line segment joining A(x , y + 1 ) and B(x + 1 , y + 2 ) is C`(3/2,5/2)`
In general to find the mid-point P(x , y) of two points `A(x_1 , y_1)` and `B (x_2 , y_ 2)` we use section formula as,
`P( x , y) = (( x_1 + x_2) / 2 , ( y _1 + y_2) /2)`
So,
`(3/2 , 5/2) =((2x + 1 ) / 2 , (2y + 3 ) /2 )`
Now equate the components separately to get,
`(2x +1)/2 = 3/2`
So,
x = 1
Similarly,
`(2y + 3)/2=5/2`
So,
y = 1
APPEARS IN
संबंधित प्रश्न
Prove that the points (−2, 5), (0, 1) and (2, −3) are collinear.
Find the third vertex of a triangle, if two of its vertices are at (−3, 1) and (0, −2) and the centroid is at the origin.
Find the points of trisection of the line segment joining the points:
(2, -2) and (-7, 4).
Find the ratio in which the point (2, y) divides the line segment joining the points A (-2,2) and B (3, 7). Also, find the value of y.
If the point C ( - 2,3) is equidistant form the points A (3, -1) and Bx (x ,8) , find the value of x. Also, find the distance between BC
`"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).`
If the vertices of ΔABC be A(1, -3) B(4, p) and C(-9, 7) and its area is 15 square units, find the values of p
If the points A(4,3) and B( x,5) lie on the circle with center O(2,3 ) find the value of x .
Points P, Q, R and S divides the line segment joining A(1, 2) and B(6, 7) in 5 equal parts. Find the coordinates of the points P, Q and R.
Write the distance between the points A (10 cos θ, 0) and B (0, 10 sin θ).
A line segment is of length 10 units. If the coordinates of its one end are (2, −3) and the abscissa of the other end is 10, then its ordinate is
If three points (0, 0), \[\left( 3, \sqrt{3} \right)\] and (3, λ) form an equilateral triangle, then λ =
If the points (k, 2k), (3k, 3k) and (3, 1) are collinear, then k
The coordinates of the fourth vertex of the rectangle formed by the points (0, 0), (2, 0), (0, 3) are
The length of a line segment joining A (2, −3) and B is 10 units. If the abscissa of B is 10 units, then its ordinates can be
A line intersects the y-axis and x-axis at P and Q , respectively. If (2,-5) is the mid-point of PQ, then the coordinates of P and Q are, respectively
Find the coordinates of the point of intersection of the graph of the equation x = 2 and y = – 3
Which of the points P(0, 3), Q(1, 0), R(0, –1), S(–5, 0), T(1, 2) do not lie on the x-axis?
Find the coordinates of the point which lies on x and y axes both.
Find the coordinates of the point whose ordinate is – 4 and which lies on y-axis.
