Question

In what ratio is the line segment joining the points A(2, 4) and B(6, 5) divided by the y-axis?

(a) 2:1 (internally)

(b) 2:1 (externally)

(c) 3:1 (internally)

(d) 3:1 (externally)

This question was addressed to me in quiz.

I want to ask this question from Geometry in portion Coordinate Geometry of Mathematics – Class 10

Answer 1

The correct answer is (d) 3:1 (externally)

Explanation: Let the ratio in which the y-axis divides the line segment joining the points A(2, 4) and B(6, 5) 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(2, 4) and B(6, 5) and the ratio is k:1

∴ x = \(\frac {k(6)+1(2)}{k+1} = \frac {6k+2}{k+1}\)

y = \(\frac {k(5)+1(4)}{k+1} = \frac {5k+4}{k+1}\)

Since, the point is on y-axis.

Hence, the x-coordinate will be zero.

∴ 0 = \(\frac {6k+2}{k+1}\)

0 = 6k + 2

k = \(\frac {-6}{2}\) = -3

The ratio in which the y-axis cuts the line segment joining the points A(2, 4) and B(6, 5) will be 3:1 (externally).