Question

Using the general points A and B, label and explain where the midpoint formula comes from.

A(x1,y1)
B(x2,y2)

Determine the midpoint of the following segments.
a) A (-4, 6) B (2,-3)

Answer 1

The midpoint formula finds the center point between two points on a Cartesian plane. For points A(-4, 6) and B(2, -3), the midpoint is calculated as M = (-1, 1.5) using the average of the respective x and y coordinates.

Step-by-step explanation:

The midpoint formula calculates the central point between two given points in a Cartesian plane. If you have points A(x1, y1) and B(x2, y2), the midpoint M is found using the formula M = ((x1 + x2)/2, (y1 + y2)/2). This formula essentially averages the x-coordinates and the y-coordinates of A and B to find the point that is exactly in the middle of them. To determine the midpoint of segment AB with A(-4, 6) and B(2, -3), you would apply the formula: Midpoint Mx = (x1 + x2)/2 = (-4 + 2)/2 = -1, Midpoint My = (y1 + y2)/2 = (6 - 3)/2 = 1.5. Therefore, the midpoint M of AB is (-1, 1.5).