Question

Show that the statement is true. If DE has endpoints D(−1, 8) and E(7, −2), then the midpoint M of DE lies in Quadrant I. The midpoint M is (

a) 3, 3
b) 3, -3
c) -3, 3
d) -3, -3

Answer 1

Using the midpoint formula, the midpoint M of the line segment DE is calculated as (3, 3), which lies in Quadrant I.

Step-by-step explanation:

The student has asked to verify if the midpoint M of the line segment DE with endpoints D(-1, 8) and E(7, -2) resides in Quadrant I and to determine its coordinates. To find the coordinates of the midpoint M, we use the midpoint formula which is [(x1 + x2)/2, (y1 + y2)/2] where (x1, y1) and (x2, y2) are the coordinates of the endpoints of the line segment.

Substituting the given values, we have the midpoint M = [(-1 + 7)/2, (8 + -2)/2] = [6/2, 6/2] = (3, 3). Since both coordinates are positive, the point (3, 3) lies in Quadrant I. Therefore, the correct answer is (a) 3, 3.