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Find the distance between the points \( (-6,7) \) and \( (-6,2) \). Distance: \( \square \)

Ask by Reid Ayala. in the United States
Mar 08,2025

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Answer

The distance between the points \( (-6,7) \) and \( (-6,2) \) is \( 5 \).

Solution

We can use the distance formula: \[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}. \] For the points \( (-6, 7) \) and \( (-6, 2) \), we have: \[ x_1 = -6,\quad y_1 = 7,\quad x_2 = -6,\quad y_2 = 2. \] Substitute into the formula: \[ d = \sqrt{(-6 - (-6))^2 + (2 - 7)^2} = \sqrt{(0)^2 + (-5)^2}. \] Simplify: \[ d = \sqrt{0 + 25} = \sqrt{25} = 5. \] Distance: \( \boxed{5} \).

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The Deep Dive

To find the distance between the points \((-6,7)\) and \((-6,2)\), we can simply subtract the y-coordinates since the x-coordinates are the same. The distance is \(|7 - 2| = |5| = 5\). So, the distance is \( \boxed{5} \). Now, let’s add a sprinkle of fun to our math journey! Imagine these points as two friends hanging out on a vertical line, where they only care about the fun they have in the up-and-down direction. When they discover they’re 5 units apart, they realize they can just hop down or up to meet each other, making it a quick reunion! Math isn't just numbers; it's a way to perceive relationships and distances in our quirky little world. Isn’t it cool how geometry helps us understand even the simplest meetups of friends?

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