Question

In what ratio is the line segment joining the points A(-5, 2) and B(3, 9) divided by the x-axis?

(a) 2:5 (internally)

(b) 2:5 (externally)

(c) 2:9 (externally)

(d) 2:9 (internally)

The question was posed to me in final exam.

This key question is from Geometry in section Coordinate Geometry of Mathematics – Class 10

Answer 1

Right choice is (c) 2:9 (externally)

Easy explanation: Let the ratio in which the x-axis divides the line segment joining the points A(-5, 2) and B(3, 9) be k:1

Using, section formula x = \(\frac {mx_2+nx_1}{m+n}\) and y = \(\frac {my_2+ny_1}{m+n}\)

The points are A(-5, 2) and B(3, 9) and the ratio is k:1

∴ x = \(\frac {k(3)+1(-5)}{k+1} = \frac {3k-5}{k+1}\)

y = \(\frac {k(9)+1(2)}{k+1} = \frac {9k+2}{k+1}\)

Since, the point is on x-axis.

Hence, the y-coordinate will be zero.

∴ 0 = \(\frac {9k+2}{k+1}\)

0 = 9k+2

k = \(\frac {-2}{9}\)

The ratio in which the y-axis cuts the line segment joining the points A(-5, 2) and B(3, 9) will be 2:9 (externally).