Answer:
The mid-point M is (2, 1). M lies in quadrant I, since the x-coordinate is positive and the y-coordinate is positive
Step-by-step explanation:
The coordinates of the midpoint (x, y) of the segment whose endpoints are (x1, y1) and (x2, y2) are x = [tex]\frac{x1+x2}{2}[/tex] , y = [tex]\frac{y1+y2}{2}[/tex]
∵ M is the midpoint of DE
∵ D = (-1, 4) and E = (5, -2)
∴ x1 = -1 and x2 = 5
∴ y1 = 4 and y2 = -2
→ Use the rule above to find x, y the coordinates of M
∵ x = [tex]\frac{-1+5}{2}[/tex] = [tex]\frac{4}{2}[/tex]
∴ x = 2
∵ y = [tex]\frac{4+-2}{2}[/tex] = [tex]\frac{2}{2}[/tex]
∴ y = 1
∴ The coordinates of the midpoint M are (2, 1)
∵ The x-coordinate is positive and the y-coordinate is positive
∴ M lies in the first quadrant (I)
The mid-point M is (2, 1). M lies in quadrant I, since the x-coordinate is positive and the y-coordinate is positive
