Advertisements
Advertisements
प्रश्न
Given a line ABCD in which AB = BC = CD, B = (0, 3) and C = (1, 8). Find the co-ordinates of A and D.
उत्तर
Given, AB = BC = CD
So, B is the mid-point of AC.
Let the co-ordinates of point A be (x, y).
∴ `(0, 3) = ((x + 1)/2, (y + 8)/2)`
`=> 0 = (x + 1)/2` and `3 = (y + 8)/2`
`=>` 0 = x + 1 and 6 = y + 8
`=>` –1 = x and –2 = y
Thus, the co-ordinates of point A are (–1, –2).
Also, C is the mid-point of BD.
Let the co-ordinates of point D be (p, q).
∴ `(1, 8) = ((0 + p)/2, (3 + q)/2)`
`=> 1 = (0 + p)/2` and `8 = (3 + q)/2`
`=>` 2 = 0 + p and 16 = 3 + q
`=>` 2 = p and 13 = q
Thus, the co-ordinates of point D are (2, 13).
APPEARS IN
संबंधित प्रश्न
Points A and B have co-ordinates (3, 5) and (x, y) respectively. The mid-point of AB is (2, 3). Find the values of x and y.
(–5, 2), (3, −6) and (7, 4) are the vertices of a triangle. Find the length of its median through the vertex (3, −6).
Calculate the co-ordinates of the centroid of the triangle ABC, if A = (7, –2), B = (0, 1) and C =(–1, 4).
M is the mid-point of the line segment joining the points A(–3, 7) and B(9, –1). Find the coordinates of point M. Further, if R(2, 2) divides the line segment joining M and the origin in the ratio p : q, find the ratio p : q.
P( -2, 5), Q(3, 6 ), R( -4, 3) and S(-9, 2) are the vertices of a quadrilateral. Find the coordinates of the midpoints of the diagonals PR and QS. Give a special name to the quadrilateral.
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.
As shown in the figure. two concentric circles are given and line AB is the tangent to the smaller circle at T. Shown that T is the midpoint of Seg AB
The centre of a circle is (−4, 2). If one end of the diameter of the circle is (−3, 7) then find the other end
The mid-point of the line joining (−a, 2b) and (−3a, −4b) is
ABC is a triangle whose vertices are A(1, –1), B(0, 4) and C(– 6, 4). D is the midpoint of BC. Find the coordinates of D.
