Find the distance between (-8, 4) and (-8, -2).
Answer (1)
Use the distance formula to find the distance between two points.
Substitute the coordinates of the points (-8, 4) and (-8, -2) into the distance formula.
Simplify the expression to find the distance.
The distance between the two points is 6 units.
Explanation
Problem Analysis We are given two points, (-8, 4) and (-8, -2), and we need to find the distance between them.
Distance Formula The distance formula is given by: d = ( 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.
Applying the Formula Let's plug in the coordinates of the given points into the distance formula: ( x 1 , y 1 ) = ( − 8 , 4 ) ( x 2 , y 2 ) = ( − 8 , − 2 ) d = ( − 8 − ( − 8 ) ) 2 + ( − 2 − 4 ) 2 d = ( 0 ) 2 + ( − 6 ) 2 d = 0 + 36 d = 36 d = 6
Final Answer The distance between the points (-8, 4) and (-8, -2) is 6 units.
Examples
In city planning, calculating the distance between two points on a map is crucial for determining the length of roads or the distance between buildings. For instance, if two buildings are located at coordinates (-8, 4) and (-8, -2) on a city grid, finding the distance between them helps in planning pedestrian walkways or utility lines. This ensures efficient urban design and resource allocation.
