Answer:
Explanation:
To find MDG, we need to calculate the length of line segment DG.
Using the distance formula, the length of a line segment between two points (x1, y1) and (x2, y2) is given by:
Distance = √((x2 - x1)^2 + (y2 - y1)^2)
Let's calculate the length of line segment DG:
DG = √((-4 - 2)^2 + (9 - 5)^2)
= √((-6)^2 + (4)^2)
= √(36 + 16)
= √52
= 2√13
Therefore, MDG is equal to 2√13.
Now, let's analyze the line segments DE and DG:
Line segment DE: The coordinates of D are (2, 5) and the coordinates of E are (-4, -4). By calculating the length of DE using the distance formula, we can determine the length of DE.
DE = √((-4 - 2)^2 + (-4 - 5)^2)
= √((-6)^2 + (-9)^2)
= √(36 + 81)
= √117
= √(9 * 13)
= 3√13
Therefore, the length of line segment DE is 3√13.
Line segment DG: We have already calculated the length of DG as 2√13.
From the calculations, we can conclude that DE and DG have different lengths. DE is 3√13 while DG is 2√13.
In summary, line segments DE and DG have different lengths.