What will be the coordinates of the point which divides the line segment joining the points A(-2, 2) and B(-1, 5) in the ratio 2:5?(a) (\(\frac {-4}{3}, \frac {-20}{9}\))(b) (\(\frac {-4}{3}, \frac {20}{9}\))(c) (\(\frac {4}{3}, \frac {20}{9}\))(d) (\(\frac {4}{3}, \frac {-20}{9}\))The question was posed to me in class test.The question is from Geometry in section Coordinate Geometry of Mathematics – Class 10

What will be the coordinates of the point which divides the line segme

1.	What will be the coordinates of the point which divides the line segment joining the points A(-2, 2) and B(-1, 5) in the ratio 2:5?(a) (\(\frac {-4}{3}, \frac {-20}{9}\))(b) (\(\frac {-4}{3}, \frac {20}{9}\))(c) (\(\frac {4}{3}, \frac {20}{9}\))(d) (\(\frac {4}{3}, \frac {-20}{9}\))The question was posed to me in class test.The question is from Geometry in section Coordinate Geometry of Mathematics – Class 10
Answer» Right choice is (b) (\(\frac {-4}{3}, \frac {20}{9}\)) Best explanation: Using, section formula x = \(\frac {mx_2+nx_1}{m+n}\) and y = \(\frac {my_2+ny_1}{m+n}\) The points are A(-2, 2) and B(-1, 5) and the RATIO is 2:5 ∴ x = \(\frac {2(-1)+5(-2)}{2+7} = \frac {-2-10}{9} = \frac {-12}{9} = \frac {-4}{3}\) y = \(\frac {2(5)+5(2)}{2+7} = \frac {10+10}{9} = \frac {20}{9} = \frac {20}{9}\) HENCE, the point is (\(\frac {-4}{3}, \frac {20}{9}\)).

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