What is the length of line segment S T if S is at negative five comma negative one and T is at negative one comma twelve? Round to the nearest hundredth.
Given points S(-5,-1) and T(-1,12)
plot the points. The segment ST is the hypotenuse of a triangle with legs of length 4 and 13.
ST = √(16+169) = √185 = 13.60
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13.60 =D
To find the length of line segment ST, we can use the distance formula in the Cartesian coordinate system. The distance formula is given by:
d = √((x2 - x1)^2 + (y2 - y1)^2)
Here, (x1, y1) represents the coordinates of point S, and (x2, y2) represents the coordinates of point T.
Let's plug in the values:
(x1, y1) = (-5, -1)
(x2, y2) = (-1, 12)
Using the distance formula, we calculate the length of ST as follows:
d = √((-1 - (-5))^2 + (12 - (-1))^2)
= √(4^2 + 13^2)
= √(16 + 169)
= √185
Thus, the length of line segment ST is √185. To round to the nearest hundredth, we can evaluate the square root to get the approximate value:
d ≈ 13.60
Therefore, the length of line segment ST is approximately 13.60 units, rounded to the nearest hundredth.