Advertisements
Advertisements
प्रश्न
If P (x, 6) is the mid-point of the line segment joining A (6, 5) and B (4, y), find y.
Advertisements
उत्तर
It is given that mid-point of line segment joining A (6, 5) and B (4, y) is P(x , 6)
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,
`(x , 6 ) = ((4+6)/2 , (y+5)/2)`
Now equate the y component to get,
`(y + 5)/2 = 6`
So,
y = 7
APPEARS IN
संबंधित प्रश्न
Prove that the points (3, 0), (6, 4) and (-1, 3) are the vertices of a right-angled isosceles triangle.
Prove that (4, 3), (6, 4) (5, 6) and (3, 5) are the angular points of a square.
If the points A (a, -11), B (5, b), C (2, 15) and D (1, 1) are the vertices of a parallelogram ABCD, find the values of a and b.
Show that the points A (1, 0), B (5, 3), C (2, 7) and D (−2, 4) are the vertices of a parallelogram.
If the point P (2,2) is equidistant from the points A ( -2,K ) and B( -2K , -3) , find k. Also, find the length of AP.
Find the area of the triangle formed by joining the midpoints of the sides of the triangle whose vertices are A(2,1) B(4,3) and C(2,5)
In what ratio does the point C (4,5) divides the join of A (2,3) and B (7,8) ?
Show that `square` ABCD formed by the vertices A(-4,-7), B(-1,2), C(8,5) and D(5,-4) is a rhombus.
\[A\left( 6, 1 \right) , B(8, 2) \text{ and } C(9, 4)\] are three vertices of a parallelogram ABCD . If E is the mid-point of DC , find the area of \[∆\] ADE.
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.
The distance between the points (a cos 25°, 0) and (0, a cos 65°) is
The ratio in which (4, 5) divides the join of (2, 3) and (7, 8) is
The ratio in which the line segment joining points A (a1, b1) and B (a2, b2) is divided by y-axis is
The point on the x-axis which is equidistant from points (−1, 0) and (5, 0) is
If P(2, 4), Q(0, 3), R(3, 6) and S(5, y) are the vertices of a parallelogram PQRS, then the value of y is
Find the point on the y-axis which is equidistant from the points (S, - 2) and (- 3, 2).
The line segment joining the points A(2, 1) and B (5, - 8) is trisected at the points P and Q such that P is nearer to A. If P also lies on the line given by 2x - y + k= 0 find the value of k.
The line 3x + y – 9 = 0 divides the line joining the points (1, 3) and (2, 7) internally in the ratio ______.
Point P(– 4, 2) lies on the line segment joining the points A(– 4, 6) and B(– 4, – 6).
Abscissa of a point is positive in ______.
