Advertisements
Advertisements
Question
Given M is the mid-point of AB, find the co-ordinates of A; if M = (1, 7) and B = (–5, 10).
Solution
M is the mid-point of AB.
Let A = (x, y), M = (1, 7) and B = (–5, 10)
∴ `1 = (x - 5)/2`
`=>` x – 5 = 2
∴ `x = 2 + 5 = 7` and `7 = (y + 10)/2`
`=>` y + 10 = 14
∴ y = 14 – 10 = 4
∴ Co-ordinates of A are (7, 4)
APPEARS IN
RELATED QUESTIONS
In the following example find the co-ordinate of point A which divides segment PQ in the ratio a : b.
P(2, 6), Q(–4, 1), a : b = 1 : 2
Find the midpoint of the line segment joining the following pair of point :
( a+3, 5b), (3a-1, 3b +4).
Two vertices of a triangle are ( -1, 4) and (5, 2). If the centroid is (0, 3), find the third vertex.
Find the mid-point of the line segment joining the points
(a, b) and (a + 2b, 2a – b)
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
If `"P"("a"/3, "b"/2)` is the mid-point of the line segment joining A(−4, 3) and B(−2, 4) then (a, b) is
The ratio in which the x-axis divides the line segment joining the points A (a1, b1) and B (a2, b2) is
In what ratio does the y-axis divides the line joining the points (−5, 1) and (2, 3) internally
Point M (2, b) is the mid-point of the line segment joining points P (a, 7) and Q (6, 5). Find the values of ‘a’ and ‘b’.
Find the coordinates of point P where P is the midpoint of a line segment AB with A(–4, 2) and B(6, 2).
Solution :
Suppose, (–4, 2) = (x1, y1) and (6, 2) = (x2, y2) and co-ordinates of P are (x, y).
∴ According to the midpoint theorem,
x = `(x_1 + x_2)/2 = (square + 6)/2 = square/2 = square`
y = `(y_1 + y_2)/2 = (2 + square)/2 = 4/2 = square`
∴ Co-ordinates of midpoint P are `square`.
