Q1. - Algebra 2

Question

Explain how you can determine in which quadrant the midpoint of the segment with endpoints at (- 6, 8) and (4, 3) lies without actually calculating the coordinates.

Step-by-Step Solution

Answer

The midpoint will be in the 2^nd quadrant.

Step 1: Analyze the x-coordinate of the midpoint

The x-coordinates of the endpoints are \(-6\) and \(4\). The midpoint's x-coordinate is the average: \(\frac{-6+4}{2} = \frac{-2}{2} = -1\). Since \(-1 < 0\), the midpoint has a negative x-coordinate.

Step 2: Analyze the y-coordinate of the midpoint

The y-coordinates are \(8\) and \(3\), both positive. Their average \(\frac{8+3}{2} = 5.5\) is also positive.

Step 3: Determine the quadrant

Since the midpoint has a negative x-coordinate and a positive y-coordinate, it lies in the second quadrant (Quadrant II). You can determine this without computing exact coordinates by noting that the average of a negative and positive x gives a negative result (since \(|-6| > |4|\)), and both y-values are positive.