Find the length of the line segment joining the points (-1, -1) and (2, 3).

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Question: Find the length of the line segment joining the points (-1, -1) and (2, 3).

Options:

Correct Answer: 5

Solution:

Length = √[(2 - (-1))² + (3 - (-1))²] = √[3² + 4²] = √25 = 5.

Find the length of the line segment joining the points (-1, -1) and (2, 3).

Find the length of the line segment joining the points (-1, -1) and (2, 3).

Correct Answer: 5

Step 1: Identify the coordinates of the two points. The first point is (-1, -1) and the second point is (2, 3).
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 = 2, and y2 = 3.
Step 4: Calculate (x2 - x1). This is (2 - (-1)) = 2 + 1 = 3.
Step 5: Calculate (y2 - y1). This is (3 - (-1)) = 3 + 1 = 4.
Step 6: Now substitute these values back into the formula: Length = √[(3)² + (4)²].
Step 7: Calculate (3)² which is 9 and (4)² which is 16.
Step 8: Add these two results together: 9 + 16 = 25.
Step 9: Finally, take the square root of 25, which is 5. This is the length of the line segment.

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