PDF chapter test TRY NOW
1. Find the coordinates of the point which divides the line segment joining the points \((3, -5)\) and \((-3, 4)\) internally, in the ratio \(1 : 2\).
Solution:
Let \(A(x_1, y_1) = (3, -5)\) , \(B(x_2, y_2) = (-3, 4)\) and \(P(x, y)\) be the required point.
Ratio, \((m : n) = 1 : 2\).
Section formula:
\(=\) \((1, -2)\)
Therefore, the coordinates of the required point are \((1, -2)\).
2. Find the ratio in which the line segment joining the points \((– 3, 10)\) and \((6, – 8)\) is divided by \((– 1, 6)\).
Solution:
Let \(A(x_1, y_1) = (-3, 10)\) , \(B(x_2, y_2) = (6, -8)\) and \(P(x, y) = (-1, 6)\).
The ratio \(m : n\) can also be written as .
That is \(k : 1\), where .
If the point \(P(x, y)\) divides the line segment in the ratio \(k : 1\), then the coordinates are:
Equate the coordinate of \(x\) values.
\(-1(k + 1) = 6k - 3\)
\(-k - 1 = 6k - 3\)
\(-1 + 3 = 6k + k\)
\(2 = 7k\)
So,
Therefore, the ratio is \(7:2\).