Question

What is the midpoint of AC given A(7, -5) and C(9, -1)?

Answer 1

The midpoint coordinates (8, -3) result from averaging the respective x and y coordinates of points A(7, -5) and C(9, -1), placing it equidistant from both endpoints. This aligns with the geometric concept of a midpoint dividing a line segment equally.The midpoint of AC, given A(7, -5) and C(9, -1), is M(8, -3).

Step-by-step explanation:

To find the midpoint of a line segment between two points, we can use the midpoint formula:

`\[ M_x = \frac{{x_1 + x_2}}{2} \]`

`\[ M_y = \frac{{y_1 + y_2}}{2} \]`

Here, A has coordinates (7, -5), and C has coordinates (9, -1). Plug these values into the midpoint formula:

`\[ M_x = \frac{{7 + 9}}{2} = 8 \]`

`\[ M_y = \frac{{-5 + (-1)}}{2} = -3 \]`

So, the midpoint M of AC is (8, -3).

In geometric terms, the midpoint is the point equidistant from both endpoints. In this case, if you consider the distance from A to M and from C to M, both distances are equal. This is consistent with the midpoint concept, as it divides the line segment into two equal parts.

Understanding the midpoint is crucial in geometry and mathematics, as it serves as a fundamental concept for various calculations and proofs. The midpoint formula is a valuable tool for finding a point that divides a line segment in a specific ratio, contributing to a deeper understanding of coordinate geometry.