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 =
`(x_(1)+x_(2))/(2)`
y midpoint =
`(y_(1)+y_(2))/(2)`

Find x midpoint, plug in the numbers
x midpoint =
`(x_(1)+x_(2))/(2)`
x midpoint =
`(5+(-2))/(2)`
x midpoint =
`(3)/(2)`
x midpoint = 1.5

Find y midpoint, plug in the numbers
y midpoint =
`(y_(1)+y_(2))/(2)`
y midpoint =
`(4+1)/(2)`
y midpoint =
`(5)/(2)`
y midpoint = 2.5

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