Question

A square ABCD has the vertices A(n, n), B(n, −n), C(−n, −n), and D(−n, n). Which vertex is in Quadrant II? Find the midpoint of the line segment defined by the points: (5, 4) and (−2, 1)

Answer 1

D is in quadrant 2. The midpoint is (1.5,2.5)

Answer 2

The one which lies in Quadrant II is D(-n,n). Quadrant II has positive y coordinate y and negative x coordinate.

Here's a way to find the midpoint
x midpoint = $\dfrac{x_{1}+x_{2}}{2}$
y midpoint = $\dfrac{y_{1}+y_{2}}{2}$

Find x midpoint, plug in the numbers
x midpoint = $\dfrac{x_{1}+x_{2}}{2}$
x midpoint = $\dfrac{5+(-2)}{2}$
x midpoint = $\dfrac{3}{2}$
x midpoint = 1.5

Find y midpoint, plug in the numbers
y midpoint = $\dfrac{y_{1}+y_{2}}{2}$
y midpoint = $\dfrac{4+1}{2}$
y midpoint = $\dfrac{5}{2}$
y midpoint = 2.5

The midpoint of the line segment is (1.5, 2.5)