Find the distance between the points $(-1.5,3.9)$ and $(-1.2,3.3)$.
Distance $\approx$
Enter your answer $\square$
$\sqrt{x}$
Give the approximate distance, rounded to three decimal places.
Answer (1)
Apply the distance formula: d = ( x 2 − x 1 ) 2 + ( y 2 − y 1 ) 2 .
Substitute the coordinates of the points: d = ( − 1.2 − ( − 1.5 ) ) 2 + ( 3.3 − 3.9 ) 2 .
Simplify the expression: d = ( 0.3 ) 2 + ( − 0.6 ) 2 = 0.09 + 0.36 = 0.45 .
Calculate the square root and round to three decimal places: d ≈ 0.671 .
Explanation
Problem Analysis We are given two points, ( − 1.5 , 3.9 ) and ( − 1.2 , 3.3 ) , and we want to find the distance between them. We will use the distance formula to calculate this distance.
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 ( x 1 , y 1 ) = ( − 1.5 , 3.9 ) and ( x 2 , y 2 ) = ( − 1.2 , 3.3 ) . Substituting these values into the distance formula, we get:
d = ( − 1.2 − ( − 1.5 ) ) 2 + ( 3.3 − 3.9 ) 2
d = ( 0.3 ) 2 + ( − 0.6 ) 2
d = 0.09 + 0.36
d = 0.45
Calculating the Distance Calculating the square root of 0.45, we get:
d ≈ 0.67082
Rounding this to three decimal places, we get:
d ≈ 0.671
Final Answer Therefore, the distance between the points ( − 1.5 , 3.9 ) and ( − 1.2 , 3.3 ) is approximately 0.671.
Examples
In navigation, you might need to calculate the distance between two GPS coordinates to determine the shortest path. Similarly, in computer graphics or game development, calculating distances between points is crucial for determining object proximity or movement paths. This concept is also fundamental in fields like urban planning, where distances between locations affect infrastructure and resource allocation.
