Advertisements
Advertisements
प्रश्न
Determine the ratio in which the line 3x + y – 9 = 0 divides the line joining (1, 3) and (2, 7).
उत्तर
Suppose the line 3x + y - 9 = 0 divides the line joining A(1, 3) and B(2, 7) in the ratio of λ: 1 at point C.
Coordinates of C = `((2λ + 1)/(λ + 1) , (7λ + 3)/(λ + 1))`
But point C lies on the line 3x + y - 9 = 0.
Therefore,
`3((2λ + 1)/(λ + 1)) + ((7λ + 3)/(λ + 1)) - 9` = 0
⇒ 6λ + 3 + 7λ + 3 - 9λ - 9 = 0
⇒ 4λ - 3 = 0
⇒ λ = `(3)/(4)`
The required ratio
= λ : 1
= 3 : 4.
APPEARS IN
संबंधित प्रश्न
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?
Find the image of the point A(5, –3) under reflection in the point P(–1, 3).
A(–4, 2), B(0, 2) and C(–2, –4) are vertices of a triangle ABC. P, Q and R are mid-points of sides BC, CA and AB respectively. Show that the centroid of ΔPQR is the same as the centroid of ΔABC.
Find the image of the point A(5,3) under reflection in the point P(-1,3).
Find the image of the point A(5,3) under reflection in the point P(-1,3).
Show that the points A(1, 3), B(2, 6), C(5, 7) and D(4, 4) are the vertices of a rhombus.
= `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.
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?
