Advertisements
Advertisements
प्रश्न
The line segment joining the points A(3, 2) and B(5, 1) is divided at the point P in the ratio 1 : 2 and it lies on the line 3x – 18y + k = 0. Find the value of k.
उत्तर
Given that, the line segment joining the points A(3, 2) and B(5, 1) is divided at the point P in the ratio 1 : 2.
∴ Coordinate of point P = `{(5(1) + 3(2))/(1 + 2), (1(1) + 2(2))/(1 + 2)}` ...`[∵ "By section formula for internal ratio" = ((m_1x_2 + m_2x_1)/(m_1 + m_2), (m_1y_2 + m_2y_1)/(m_1 + m_2))]`
= `((5 + 6)/3, (1 + 4)/3)`
= `(11/3, 5/3)`
But the point `P(11/3, 5/3)` lies on the line 3x – 18y + k = 0 ...[Given]
∴ `3(11/3) - 18(5/8) + k` = 0
⇒ 11 – 30 + k = 0
⇒ k – 19 = 0
⇒ k = 19
Hence, the required value of k is 19.
APPEARS IN
संबंधित प्रश्न
Find the ratio in which the point P(x, 2) divides the line segment joining the points A(12, 5) and B(4, −3). Also, find the value of x.
If A(–2, –1), B(a, 0), C(4, b) and D(1, 2) are the vertices of a parallelogram, find the values of a and b
Find the ratio in which the line segment joining the points (-3, 10) and (6, -8) is divided by (-1, 6).
If two vertices of a parallelogram are (3, 2) (-1, 0) and the diagonals cut at (2, -5), find the other vertices of the parallelogram.
Find the length of the medians of a ΔABC having vertices at A(0, -1), B(2, 1) and C(0, 3).
Calculate the ratio in which the line joining A(6, 5) and B(4, –3) is divided by the line y = 2.
If the coordinates of one end of a diameter of a circle are (2, 3) and the coordinates of its centre are (−2, 5), then the coordinates of the other end of the diameter are:
Show that the lines x = O and y = O trisect the line segment formed by joining the points (-10, -4) and (5, 8). Find the points of trisection.
Find the ratio in which the point `P(3/4, 5/12)` divides the line segment joining the points `A(1/2, 3/2)` and B(2, –5).
Read the following passage:
Jagdish has a field which is in the shape of a right angled triangle AQC. He wants to leave a space in the form of a square PQRS inside the field for growing wheat and the remaining for growing vegetables (as shown in the figure). In the field, there is a pole marked as O. |
Based on the above information, answer the following questions :
- Taking O as origin, coordinates of P are (–200, 0) and of Q are (200, 0). PQRS being a square, what are the coordinates of R and S?
- (a) What is the area of square PQRS?
OR
(b) What is the length of diagonal PR in square PQRS? - If S divides CA in the ratio K : 1, what is the value of K, where point A is (200, 800)?
