If point D(3, 4) is the midpoint of segment AB where A(1, 2) and B(x, y), what a

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Question: If point D(3, 4) is the midpoint of segment AB where A(1, 2) and B(x, y), what are the coordinates of B?

Options:

Correct Answer: (5, 6)

Solution:

Using the midpoint formula: D = ((x1 + x2)/2, (y1 + y2)/2). Solving gives B = (5, 6).

If point D(3, 4) is the midpoint of segment AB where A(1, 2) and B(x, y), what are the coordinates of B?

If point D(3, 4) is the midpoint of segment AB where A(1, 2) and B(x, y), what are the coordinates of B?

Step 1: Identify the coordinates of point D, which is the midpoint. D = (3, 4).
Step 2: Identify the coordinates of point A. A = (1, 2).
Step 3: Let the coordinates of point B be (x, y).
Step 4: Use the midpoint formula: D = ((x1 + x2)/2, (y1 + y2)/2). Here, (x1, y1) are the coordinates of A and (x2, y2) are the coordinates of B.
Step 5: Substitute the known values into the midpoint formula: D = ((1 + x)/2, (2 + y)/2).
Step 6: Set the x-coordinates equal: (1 + x)/2 = 3.
Step 7: Multiply both sides by 2 to eliminate the fraction: 1 + x = 6.
Step 8: Solve for x: x = 6 - 1, so x = 5.
Step 9: Set the y-coordinates equal: (2 + y)/2 = 4.
Step 10: Multiply both sides by 2: 2 + y = 8.
Step 11: Solve for y: y = 8 - 2, so y = 6.
Step 12: Therefore, the coordinates of point B are (5, 6).

Midpoint Formula – The midpoint formula is used to find the midpoint of a line segment given the coordinates of its endpoints.
Coordinate Geometry – Understanding how to manipulate and solve for coordinates in a Cartesian plane.