Question

bar (PQ) has endpoints P(-4,1) and Q(2,-3). Use the Midpoint Formula to find the midpoint of bar (PQ). What Quadrant does the midpoint lie in?

Answer 1

The midpoint of bar (PQ) is (-1, -1), and it lies in Quadrant III.

Step-by-step explanation:

`The Midpoint Formula is given by the coordinates (x, y) = \(\left(\frac{{x_1 + x_2}}{2}, \frac{{y_1 + y_2}}{2}\right)\), where (x1, y1) and (x2, y2) are the coordinates of the endpoints P and Q, respectively. In this case, P(-4, 1) and Q(2, -3)`.

Applying the Midpoint Formula, we get:

`\[ x = \frac{{-4 + 2}}{2} = -1 \]\[ y = \frac{{1 + (-3)}}{2} = -1 \]`

Therefore, the midpoint of bar (PQ) is (-1, -1). To determine the quadrant in which the midpoint lies, we consider the signs of the x and y coordinates. Since both x and y are negative, the point (-1, -1) is in Quadrant III.

In Quadrant III, both x and y coordinates are negative. This means that the midpoint of bar (PQ) is positioned to the left of the origin (negative x) and below the origin (negative y). Understanding the quadrant helps provide a visual representation of the location of the midpoint on the coordinate plane.