Find the distance between the points (-5, -10) and (2, 4).
4.58
12.12
15.65
21
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To find the distance between the points (-5, -10) and (2, 4), we can use the distance formula:
[
d = sqrt{(x_2 – x_1)^2 + (y_2 – y_1)^2}
]
Where ((x_1, y_1) = (-5, -10)) and ((x_2, y_2) = (2, 4)).
Now, let’s plug in the values:
1. Calculate (x_2 – x_1):
[
2 – (-5) = 2 + 5 = 7
]
2. Calculate (y_2 – y_1):
[
4 – (-10) = 4 + 10 = 14
]
3. Substitute these into the distance formula:
[
d = sqrt{(7)^2 + (14)^2}
]
[
d = sqrt{49 + 196}
]
[
d = sqrt{245}
]
[
d approx 15.65
]
So, the distance between the two points is approximately 15.65.
To find the distance between the points ((-5, -10)) and ((2, 4)), we can use the distance formula:
[
d = sqrt{(x_2 – x_1)^2 + (y_2 – y_1)^2}
]
Where ((x_1, y_1)) and ((x_2, y_2)) are the coordinates of the two points.
1. Here, ((x_1, y_1) = (-5, -10)) and ((x_2, y_2) = (2, 4)).
2. Calculate the differences:
– (x_2 – x_1 = 2 – (-5) = 2 + 5 = 7)
– (y_2 – y_1 = 4 – (-10) = 4 + 10 = 14)
3. Now plug these values into the formula:
[
d = sqrt{(7)^2 + (14)^2} = sqrt{49 + 196} = sqrt{245}
]
4. Finally, simplify (sqrt{245}):
[
sqrt{245} = sqrt{49 times 5} = 7sqrt{5} approx 15.65
]
Therefore, the distance between the points