Question

In what ratio the line segment joining the points (-2, 3) and (3, -7) is divided by x-axis ?

• A. 2 : 3
• B. 3 : 2
• C. 3 : 7
• D. 1 : 4

Answer 1

The Correct Option is C

To find the ratio in which the x-axis divides the line segment joining the points \((-2, 3)\) and \( (3, -7) \), we need to use the section formula. The x-axis divides a line segment where the \(y\)-coordinate of the dividing point is \(0\). Let's denote this point as \(P(x, 0)\). The section formula in terms of a ratio \(m:n\) for coordinates \((x_1, y_1)\) and \((x_2, y_2)\) is given by:

\[(x, y) = \left(\frac{mx_2 + nx_1}{m+n}, \frac{my_2 + ny_1}{m+n}\right)\]

Given points are \((-2, 3)\) and \( (3, -7)\). We know \(y = 0\) at the point dividing the line on the x-axis:

\[0 = \frac{m(-7) + n(3)}{m+n}\]

Solving for the ratio \(m:n\):

\[m(-7) + n(3) = 0\]

\[-7m + 3n = 0\]

\[3n = 7m\]

\[\frac{m}{n} = \frac{3}{7}\]

Thus, the x-axis divides the line segment in the ratio \(3:7\).

Therefore, the correct option is 3:7.