Final answer:
To find the length of the line segment DG, we can use the midpoint formula and the distance formula.
Step-by-step explanation:
To find the length of a line segment, we need to use the midpoint formula. The midpoint formula is given by:
(x1 + x2) / 2, (y1 + y2) / 2
Where (x1, y1) and (x2, y2) are the coordinates of the endpoints of the line segment. In this case, (x1, y1) = (-2, 13) and the midpoint (x2, y2) = (-18, 5).
Using the midpoint formula, we can calculate the coordinates of the second endpoint. Let's call the coordinates of the second endpoint (x, y). We have:
(-2 + x) / 2 = -18 => -2 + x = -36 => x = -34
(13 + y) / 2 = 5 => 13 + y = 10 => y = -3
So, the coordinates of the second endpoint are (-34, -3). Now, we can use the distance formula to find the length of the line segment using the coordinates of the two endpoints:
d = sqrt((x2 - x1)2 + (y2 - y1)2)
Plugging in the values:
d = sqrt((-34 - (-2))2 + (-3 - 13)2)
d = sqrt((-34 + 2)2 + (-3 - 13)2)
d = sqrt((-32)2 + (-16)2)
d = sqrt(1024 + 256)
d = sqrt(1280)
d ≈ 35.78
The measure closest to the length of DG is approximately 35.78.
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