Question
Find the distance between the pair of points. \( N(-3,-14), P(-3,-2) \) \( d=\square \) (Simplify your answer. Type an exact answer, using radicals as needed.)
Ask by Johnson Bryant. in the United States
Feb 04,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The distance between the points \( N(-3, -14) \) and \( P(-3, -2) \) is 12 units.
Solution
The points \( N(-3, -14) \) and \( P(-3, -2) \) share the same \( x \)-coordinate, which means they lie on the same vertical line. To find the distance between them, you simply calculate the difference in their \( y \)-coordinates.
\[
d = |-14 - (-2)| = |-14 + 2| = | -12 | = 12
\]
So, the distance between the points is:
\[
d = 12
\]
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Simplify this solution Beyond the Answer
To find the distance between the points \( N(-3,-14) \) and \( P(-3,-2) \), we can use the distance formula: \[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \] Plugging in the coordinates of points \( N \) and \( P \): \[ d = \sqrt{((-3) - (-3))^2 + ((-2) - (-14))^2} \] This simplifies to: \[ d = \sqrt{(0)^2 + (12)^2} = \sqrt{0 + 144} = \sqrt{144} = 12 \] So, the distance \( d \) is \( 12 \).
