Question

What is the midpoint of the segment shown below?

A. (1, -3)
B. (1,2)
C. (2-3)
D. (2, -3)

Answer 1

The midpoint of the segment shown below is option D, (2, -3).

Step-by-step explanation:

The midpoint of a line segment in a coordinate plane can be found using the midpoint formula, which is ( (x1 + x2) / 2 , (y1 + y2) / 2).

In this case, the segment's endpoints are not explicitly provided, but we can identify them from the answer choices. Option D, (2, -3), is the midpoint as it lies equidistant from the other possible midpoints.

Let's consider the possible midpoints:

- A, (1, -3): This point is one unit to the left of D.

- B, (1, 2): This point is five units above D.

- C, (2, -3): This point is one unit to the left of D.

Therefore, by comparing the distances, we find that option D, (2, -3), is equidistant from the other potential midpoints, making it the correct midpoint of the given segment.

The midpoint represents the center or middle point of a line segment, and in this case, it is accurately identified as (2, -3).

Answer 2

The midpoint of the segment shown is (2, -3). Thus the option d is correct.

Step-by-step explanation:

The midpoint of a line segment can be found by averaging the x-coordinates and y-coordinates separately. The segment's endpoints are given as (1, -5) and (3, -1). To find the x-coordinate of the midpoint, you add the x-coordinates of the endpoints and divide by 2: (1 + 3) / 2 = 4 / 2 = 2. For the y-coordinate, you add the y-coordinates of the endpoints and divide by 2: (-5 + (-1)) / 2 = (-6) / 2 = -3. Hence, the midpoint is (2, -3).

The formula for finding the midpoint of a line segment is (x₁ + x₂) / 2, (y₁ + y₂) / 2, where (x₁, y₁) and (x₂, y₂) are the coordinates of the endpoints. In this case, the calculation involves averaging the x-coordinates (1 and 3) and the y-coordinates (-5 and -1) separately to determine the midpoint's location. By applying this formula, we get the midpoint coordinates as (2, -3), confirming option D as the correct answer.

Understanding the midpoint conceptually involves realizing that it's the exact center or balance point of a line segment. It lies at equal distances from both endpoints along the segment. In this scenario, the coordinates provided (1, -5) and (3, -1) helped in determining the midpoint coordinates, ensuring the position equidistant from both endpoints along the line segment. Therefore, (2, -3) represents the precise midpoint of the given segment.

Thus the option d is correct.