NCERT Exemplar Solutions
Class 10 - Mathematics - CHAPTER 7: Coordinate Geometry - Exercise 7.1

Question 9

Step 1: Recall the section formula.

If a point divides a line joining \((x_1, y_1)\) and \((x_2, y_2)\) in the ratio \(m:n\), then its coordinates are:

\(P = \Big( \dfrac{mx_2 + nx_1}{m+n},\; \dfrac{my_2 + ny_1}{m+n} \Big)\).

Step 2: Here, ratio is \(1:2\), so \(m=1\) and \(n=2\).

Given points: \((x_1, y_1) = (7, -6)\) and \((x_2, y_2) = (3, 4)\).

Step 3: Find x-coordinate of P.

\(x = \dfrac{1 \cdot 3 + 2 \cdot 7}{1+2} = \dfrac{3 + 14}{3} = \dfrac{17}{3}\).

So, \(x = \dfrac{17}{3} > 0\).

Step 4: Find y-coordinate of P.

\(y = \dfrac{1 \cdot 4 + 2 \cdot (-6)}{1+2} = \dfrac{4 - 12}{3} = \dfrac{-8}{3}\).

So, \(y = -\dfrac{8}{3} < 0\).

Step 5: Decide the quadrant.

Since \(x > 0\) and \(y < 0\), the point lies in the IV quadrant.