Which of the following points is equidistant from the points (1, 2) and (3, 4)?

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Question: Which of the following points is equidistant from the points (1, 2) and (3, 4)?

Options:

Correct Answer: (2, 3)

Solution:

The point (2, 3) is the midpoint of the segment joining (1, 2) and (3, 4), making it equidistant from both.

Which of the following points is equidistant from the points (1, 2) and (3, 4)?

Which of the following points is equidistant from the points (1, 2) and (3, 4)?

Step 1: Identify the two points given in the question: Point A is (1, 2) and Point B is (3, 4).
Step 2: To find a point that is equidistant from both points, we need to find the midpoint of the line segment connecting Point A and Point B.
Step 3: Use the midpoint formula, which is: Midpoint = ((x1 + x2) / 2, (y1 + y2) / 2). Here, (x1, y1) is Point A and (x2, y2) is Point B.
Step 4: Plug in the coordinates: Midpoint = ((1 + 3) / 2, (2 + 4) / 2).
Step 5: Calculate the x-coordinate: (1 + 3) / 2 = 4 / 2 = 2.
Step 6: Calculate the y-coordinate: (2 + 4) / 2 = 6 / 2 = 3.
Step 7: The midpoint is (2, 3), which is equidistant from both points (1, 2) and (3, 4).

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