Advertisements
Advertisements
प्रश्न
The mid-point of the line segment joining (2a, 4) and (–2, 2b) is (1, 2a + 1). Find the values of a and b.
उत्तर
Mid-point of (2a, 4) and (−2, 2b) is (1, 2a + 1),
Therefore using mid-point formula, we have:
`x = (x_1 + x_2)/2 `
`1 = (2a - 2)/2`
1 = a − 1
a = 2
` y = (y_1 + y_2)/2`
`2a + 1 = (4 + 2b)/2`
2a + 1 = 2 + b
2 × 2 + 1 – 2 = b
b = 5 – 2 = 3
Therefore, a = 2, b = 3.
APPEARS IN
संबंधित प्रश्न
A(5, x), B(−4, 3) and C(y, –2) are the vertices of the triangle ABC whose centroid is the origin. Calculate the values of x and y.
In the following example find the co-ordinate of point A which divides segment PQ in the ratio a : b.
P(–2, –5), Q(4, 3), a : b = 3 : 4
Find th co-ordinates of the midpoint of the line segment joining P(0, 6) and Q(12, 20).
Find the midpoint of the line segment joining the following pair of point :
( a+3, 5b), (3a-1, 3b +4).
Find the midpoint of the line segment joining the following pair of point :
(a+b, b-a) and (a-b, a+b)
If (-3, 2), (1, -2) and (5, 6) are the midpoints of the sides of a triangle, find the coordinates of the vertices of the triangle.
A , B and C are collinear points such that AB = `1/2` AC . If the coordinates of A, B and C are (-4 , -4) , (-2 , b) anf (a , 2),Find the values of a and b.
A(3, 1), B(y, 4) and C(1, x) are vertices of a triangle ABC and G(3, 4) is its centroid. Find the values of x and y. Also, find the length of side BC.
The mid-point of the sides of a triangle are (2, 4), (−2, 3) and (5, 2). Find the coordinates of the vertices of the triangle
In what ratio does the point Q(1, 6) divide the line segment joining the points P(2, 7) and R(−2, 3)
