Question

The mid-point of the line segment joining the points \( (-2, 8) \) and \( (-6, -4) \) lies in which quadrant?

• A. First
• B. Second
• C. Third
• D. Fourth

Hint:

Quadrant signs: I \((+,+)\), II \((-,+)\), III \((-,-)\), IV \((+,-)\). For midpoints, average the coordinates component-wise.

Answer 1

The Correct Option is B

Step 1: Use the midpoint formula.
Midpoint \(M\) of \( (x_1,y_1) \) and \( (x_2,y_2) \) is \( M\left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right). \)
Step 2: Substitute the given points.
\[ M\left(\frac{-2+(-6)}{2}, \frac{8+(-4)}{2}\right) = \left(\frac{-8}{2}, \frac{4}{2}\right) = (-4, 2). \]
Step 3: Identify the quadrant.
Since \(x<0\) and \(y>0\), the point \((-4,2)\) lies in the Second quadrant.