Problem 1 :
Find the ratio in which the point (11, 15) divides the line segment joining the point (15, 5) and (9, 20).
Solution:
Given points are (15, 5) and (9, 20).
Let P(11, 15) divide AB internally in the ratio l : m.
By the section formula,
Equating the coefficients of x, we get
Hence, the point divides the line segment joining the points in the ratio 4 : 2.
Problem 2 :
Find the ratio in which the point P(m, 6) divides the line segment joining the point A(-4, 3) and B(2, 8). Also find the value of m.
Solution:
Using the section formula, if a point (x, y) divided the line joining the points (x_{1}, y_{1}) and (x_{2}, y_{2}) in the ratio l : m, then
Let P divides the join of A and B in the ratio k : 1, then
Therefore, we have
Problem 3 :
Find the ratio in which the point P(-6, a) divides the join of A(-3, -1) and B(-8, 9). Also find the value of a.
Solution:
Using the section formula, if a point (x, y) divided the line joining the points (x_{1}, y_{1}) and (x_{2}, y_{2}) in the ratio l : m, then
l : m = 3 : 2
To find a, equating the coefficient of y
Problem 4 :
Find the ratio in which the point P(-3, a) divides the join of A(-5, -4) and B(-2, 3). Also find the value of a.
Solution:
Using the section formula, if a point (x, y) divided the line joining the points (x_{1}, y_{1}) and (x_{2}, y_{2}) in the ratio l : m, then
To find a, equating the coefficient of y
Problem 5 :
Find the ratio in which the point P(a, 1) divides the join of A(-4, 4) and B(6, -1). Also find the value of a.
Solution:
Using the section formula, if a point (x, y) divided the line joining the points (x_{1}, y_{1}) and (x_{2}, y_{2}) in the ratio l : m, then
To find a, equating the coefficient of x
Problem 6 :
Find the ratio in which the line segment joining the points (-3, 10) and (6, -8) is divided by (-1, 6).
Solution:
Hence, the point divides the line segment joining the points in the ratio 2 : 7.
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