Find the distance between the points (1, 2) and (4, 6).
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Step-by-Step Solution
Step 1: Identify the coordinates
First, we identify the coordinates of the two given points. Let the first point be (x1,y1) and the second point be (x2,y2).
Step 2: Recall the Distance Formula
To find the distance between two points in a coordinate plane, we use the distance formula. This formula is derived from the Pythagorean theorem.
Step 3: Substitute the coordinates into the formula
Now, we substitute the identified coordinates into the distance formula. We replace x1 with 1, y1 with 2, x2 with 4, and y2 with 6.
Step 4: Calculate the differences
Next, we perform the subtractions inside the parentheses: 4−1=3 and 6−2=4.
Step 5: Square the differences and add
Now, we square the results: 32=9 and 42=16. Then, we add these squared values together: 9+16=25.
Step 6: Calculate the square root
Finally, we take the square root of 25, which gives us 5. This is the distance between the two given points.