If the midpoint of a line segment is (4, 5) and one endpoint is (2, 3), what is

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Question: If the midpoint of a line segment is (4, 5) and one endpoint is (2, 3), what is the other endpoint?

Options:

Correct Answer: (6, 7)

Solution:

Let the other endpoint be (x, y). The midpoint formula gives (2 + x)/2 = 4 and (3 + y)/2 = 5. Solving these gives x = 6 and y = 7.

If the midpoint of a line segment is (4, 5) and one endpoint is (2, 3), what is the other endpoint?

If the midpoint of a line segment is (4, 5) and one endpoint is (2, 3), what is the other endpoint?

Step 1: Understand that the midpoint of a line segment is the average of the x-coordinates and the average of the y-coordinates of the endpoints.
Step 2: Identify the given midpoint, which is (4, 5), and one endpoint, which is (2, 3).
Step 3: Let the other endpoint be (x, y).
Step 4: Use the midpoint formula for the x-coordinates: (2 + x) / 2 = 4.
Step 5: Multiply both sides of the equation from Step 4 by 2 to eliminate the fraction: 2 + x = 8.
Step 6: Subtract 2 from both sides of the equation from Step 5 to solve for x: x = 6.
Step 7: Use the midpoint formula for the y-coordinates: (3 + y) / 2 = 5.
Step 8: Multiply both sides of the equation from Step 7 by 2: 3 + y = 10.
Step 9: Subtract 3 from both sides of the equation from Step 8 to solve for y: y = 7.
Step 10: Combine the values of x and y to find the other endpoint: (6, 7).

Midpoint Formula – The midpoint of a line segment is calculated as the average of the x-coordinates and the average of the y-coordinates of the endpoints.