Peters Rojas
03/07/2024 · Primary School
Calculate the distance between the points \( L=(2,-3) \) and \( Q=(7,-9) \) in the coordinate plane. Round your answer to the nearest hundredth.
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Step-by-step Solution
To calculate the distance between the points \( L = (2, -3) \) and \( Q = (7, -9) \), we can use the distance formula:
\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]
Here, \( (x_1, y_1) = (2, -3) \) and \( (x_2, y_2) = (7, -9) \).
Now, we can substitute the coordinates into the formula:
\[
d = \sqrt{(7 - 2)^2 + (-9 - (-3))^2}
\]
Calculating the differences:
\[
x_2 - x_1 = 7 - 2 = 5
\]
\[
y_2 - y_1 = -9 - (-3) = -9 + 3 = -6
\]
Now, we can substitute these values back into the distance formula:
\[
d = \sqrt{(5)^2 + (-6)^2}
\]
Calculating the squares:
\[
d = \sqrt{25 + 36}
\]
Adding the squares:
\[
d = \sqrt{61}
\]
Now, we can calculate \( \sqrt{61} \):
\[
\sqrt{61} \approx 7.8102
\]
Rounding to the nearest hundredth, we get:
\[
d \approx 7.81
\]
Thus, the distance between the points \( L \) and \( Q \) is approximately \( \boxed{7.81} \).
Quick Answer
The distance between the points \( L=(2,-3) \) and \( Q=(7,-9) \) is approximately 7.81.
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