Find the distance between the points A(5, 9) and B(3, 11).
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Step-by-Step Solution
Step 1: Identify the coordinates
First, we identify the coordinates of the two given points. Point A has coordinates (x1,y1)=(5,9) and Point B has coordinates (x2,y2)=(3,11). These values will be used in the distance formula.
Step 2: Apply the distance formula
To find the distance between two points in a Cartesian plane, we use the distance formula. This formula is derived from the Pythagorean theorem and calculates the length of the line segment connecting the two points.
Step 3: Substitute the values
Now, we substitute the identified coordinates into the distance formula. We replace x1 with 5, y1 with 9, x2 with 3, and y2 with 11.
Step 4: Calculate the differences
Next, we perform the subtractions inside the parentheses. (3−5) becomes −2, and (11−9) becomes 2.
Step 5: Square the differences
Now, we square the results from the previous step. (−2)2 is 4, and (2)2 is also 4.
Step 6: Sum and find the square root
Finally, we sum the squared values to get 8, and then find the square root of 8. The square root of 8 can be simplified to 22.