Find the length of the line segment joining the points (1, 1) and (4, 5).

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Question: Find the length of the line segment joining the points (1, 1) and (4, 5).

Options:

Correct Answer: 5

Solution:

Length = √[(4-1)² + (5-1)²] = √[3² + 4²] = √[9 + 16] = √25 = 5.

Find the length of the line segment joining the points (1, 1) and (4, 5).

Find the length of the line segment joining the points (1, 1) and (4, 5).

Step 1: Identify the coordinates of the two points. The first point is (1, 1) and the second point is (4, 5).
Step 2: Use the distance formula to find the length of the line segment. The formula is Length = √[(x2 - x1)² + (y2 - y1)²].
Step 3: Substitute the coordinates into the formula. Here, x1 = 1, y1 = 1, x2 = 4, and y2 = 5.
Step 4: Calculate (x2 - x1). This is (4 - 1) = 3.
Step 5: Calculate (y2 - y1). This is (5 - 1) = 4.
Step 6: Square the results from Step 4 and Step 5. So, 3² = 9 and 4² = 16.
Step 7: Add the squared results together. This is 9 + 16 = 25.
Step 8: Take the square root of the sum from Step 7. √25 = 5.
Step 9: The length of the line segment joining the points (1, 1) and (4, 5) is 5.

Distance Formula – The distance between two points in a Cartesian plane is calculated using the formula √[(x2 - x1)² + (y2 - y1)²].