If point C(4, 5) is the midpoint of segment AB, and A is at (2, 3), what are the

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Question: If point C(4, 5) is the midpoint of segment AB, and A is at (2, 3), what are the coordinates of point B?

Options:

Correct Answer: (6, 7)

Solution:

Using the midpoint formula: B = (2*C - A) = (2*4 - 2, 2*5 - 3) = (6, 7).

If point C(4, 5) is the midpoint of segment AB, and A is at (2, 3), what are the coordinates of point B?

If point C(4, 5) is the midpoint of segment AB, and A is at (2, 3), what are the coordinates of point B?

Step 1: Understand that point C(4, 5) is the midpoint of segment AB.
Step 2: Recall the coordinates of point A, which are (2, 3).
Step 3: Use the midpoint formula, which states that the midpoint C is the average of the coordinates of points A and B.
Step 4: The formula for the midpoint is: C = ((x_A + x_B)/2, (y_A + y_B)/2).
Step 5: Substitute the known values into the formula: C(4, 5) = ((2 + x_B)/2, (3 + y_B)/2).
Step 6: Set up two equations based on the x-coordinates and y-coordinates: 4 = (2 + x_B)/2 and 5 = (3 + y_B)/2.
Step 7: Solve the first equation for x_B: Multiply both sides by 2 to get 8 = 2 + x_B, then subtract 2 from both sides to find x_B = 6.
Step 8: Solve the second equation for y_B: Multiply both sides by 2 to get 10 = 3 + y_B, then subtract 3 from both sides to find y_B = 7.
Step 9: Combine the results to find the coordinates of point B: B = (6, 7).

Midpoint Formula – The midpoint of a segment AB is calculated as M = ((x1 + x2)/2, (y1 + y2)/2), where M is the midpoint and A(x1, y1) and B(x2, y2) are the endpoints.
Coordinate Geometry – Understanding how to manipulate and calculate coordinates in a Cartesian plane.