What is the vertical distance between (5, -12) and (5, 17)?
Answer (2)
The problem asks for the vertical distance between two points.
The vertical distance is found by calculating the absolute difference in the y-coordinates: ∣ y 2 − y 1 ∣ .
Substitute the given y-coordinates: ∣17 − ( − 12 ) ∣ = ∣17 + 12∣ = ∣29∣ .
The vertical distance is: 29 units .
Explanation
Analyze the problem We are given two points, (5, -12) and (5, 17), and we want to find the vertical distance between them. The vertical distance is the absolute difference in their y-coordinates.
State the formula and given points The formula for the vertical distance between two points ( x 1 , y 1 ) and ( x 2 , y 2 ) is ∣ y 2 − y 1 ∣ . In our case, ( x 1 , y 1 ) = ( 5 , − 12 ) and ( x 2 , y 2 ) = ( 5 , 17 ) . So, we need to calculate ∣17 − ( − 12 ) ∣ .
Calculate the distance Now, let's calculate the vertical distance:
∣17 − ( − 12 ) ∣ = ∣17 + 12∣ = ∣29∣ = 29
The vertical distance between the two points is 29 units.
State the final answer Therefore, the vertical distance between the points (5, -12) and (5, 17) is 29 units.
Examples
Understanding vertical distance is crucial in many real-world applications. For example, in architecture, when designing a staircase, you need to calculate the vertical distance (rise) between each step to ensure it meets safety standards and is comfortable to use. Similarly, in geography, determining the vertical distance between different points on a map helps in understanding elevation changes and planning routes.
The vertical distance between the points (5, -12) and (5, 17) is 29 units, calculated by finding the absolute difference between their y-coordinates. This is done using the formula ∣ y 2 − y 1 ∣ .
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