If the midpoint of a line segment joining points A(1, 2) and B(x, y) is M(3, 4),

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Question: If the midpoint of a line segment joining points A(1, 2) and B(x, y) is M(3, 4), what is the value of x?

Options:

Correct Answer: 6

Solution:

The midpoint M is given by M = ((x1 + x2)/2, (y1 + y2)/2). Setting up the equations: (1 + x)/2 = 3 gives x = 5.

If the midpoint of a line segment joining points A(1, 2) and B(x, y) is M(3, 4), what is the value of x?

If the midpoint of a line segment joining points A(1, 2) and B(x, y) is M(3, 4), what is the value of x?

Step 1: Identify the coordinates of points A and B. A is (1, 2) and B is (x, y).
Step 2: Identify the coordinates of the midpoint M, which is given as (3, 4).
Step 3: Use the formula for the midpoint: M = ((x1 + x2)/2, (y1 + y2)/2). Here, x1 = 1, y1 = 2, x2 = x, and y2 = y.
Step 4: Set up the equation for the x-coordinates: (1 + x)/2 = 3.
Step 5: Multiply both sides of the equation by 2 to eliminate the fraction: 1 + x = 6.
Step 6: Subtract 1 from both sides to solve for x: x = 6 - 1.
Step 7: Calculate the value of x: x = 5.

Midpoint Formula – The midpoint of a line segment is calculated using the formula M = ((x1 + x2)/2, (y1 + y2)/2), where (x1, y1) and (x2, y2) are the coordinates of the endpoints.