Question

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 1

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 (\(\frac {-4}{3}, \frac {20}{9}\)).