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प्रश्न
The midpoint of the line segment AB shown in the diagram is (4, – 3). Write down the coordinates of A and B.
उत्तर
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).
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= `a(1/t^2 + 1) = (a(t^2 + 1))/t^2`
Now `(1)/"SP" + (1)/"SQ" = (1)/(a(t^2 + 1)) + (1 xx t^2)/(a(t^2 + 1)`
= `((1 + t^2))/(a(t^2 + 1)`
`(1)/"SP" + (1)/"SQ" = (1)/a`.
If the line joining the points A(4, - 5) and B(4, 5) is divided by the point P such that `"AP"/"AB" = (2)/(5)`, find the coordinates of P.
In the following figure line APB meets the X-axis at A, Y-axis at B. P is the point (4, -2) and AP: PB = 1: 2. Write down the coordinates of A and B.
