Advertisements
Advertisements
Question
The midpoint of the line segment AB shown in the diagram is (4, – 3). Write down the coordinates of A and B.
Solution
Let the coordinates of A and Bare (x, 0) and (0, y).
so `x = (mx_2 + nx_1)/(m + n), y = (my_2 + ny_1)/(m + n)`|
m = 2, n = 3
x1 = 4, x2 = 4
y1 = -5, y2 = 5
∴ x = `(2 xx 4 + 3 xx 4)/(2 + 3) = (8 + 12)/(5) = (20)/(5)` = 4
y = `(2 xx 5 + 3 xx- 5)/(2 + 3)`
= `(10 - 15)/(5)`
= `(-5)/(5)`
= -1
∴ Co-ordinates of P are (4, -1).
Thus, the coordinates of midpoints of
AB = `((x + 2)/2, (y + 0)/2)`
= `(x/2 , y/2)`
According to question, the coordinates of midpoint = (4, -3)
∴ `x/(2)` = 4, x = 8
`y/(2)` = -3, y = -6
∴ The required points are (9, 0) and (0, -6).
APPEARS IN
RELATED QUESTIONS
P(1, -2) is a point on the line segment A(3, -6) and B(x, y) such that AP : PB is equal to 2 : 3. Find the coordinates of B.
Calculate the co-ordinates of the point P which divides the line segment joining: A (–4, 6) and B (3, –5) in the ratio 3 : 2
In what ratio is the line joining (2, –3) and (5, 6) divided by the x-axis?
Calculate the ratio in which the line joining A(-4,2) and B(3,6) is divided by point p(x,3). Also, find x
M is the mid-point of the line segment joining the points A(0, 4) and B(6, 0). M also divides the line segment OP in the ratio 1 : 3. Find :
- co-ordinates of M
- co-ordinates of P
- length of BP
Find the image of the point A(5, –3) under reflection in the point P(–1, 3).
The line segment joining A (2, 3) and B (6, – 5) is intersected by the X axis at the point K. Write the ordinate of the point K. Hence find the ratio in which K divides AB.
Determine the ratio in which the line 3x + y – 9 = 0 divides the line joining (1, 3) and (2, 7).
Determine the centre of the circle on which the points (1, 7), (7 – 1), and (8, 6) lie. What is the radius of the circle?
From the adjacent figure:
(i) Write the coordinates of the points A, B, and
(ii) Write the slope of the line AB.
(iii) Line through C, drawn parallel to AB, intersects Y-axis at D. Calculate the co-ordinates of D.
