BR 12/5/23 Midpoint & Distance Formula Assignment

The Midpoint Formula is used to find the midpoint of a line segment with endpoints (x1, y1) and (x2, y2). It is given by: $$M = \left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right)$$ .

The Distance Formula is used to find the distance between two points (x1, y1) and (x2, y2). It is given by: $$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$ .

The midpoint is $$M = \left(\frac{6 + 6}{2}, \frac{7 + (-5)}{2}\right) = (6, 1)$$ .

The distance is $$d = \sqrt{(5 - (-3))^2 + (5 - (-4))^2} = \sqrt{8^2 + 9^2} = \sqrt{64 + 81} = \sqrt{145} \approx 12$$ .

The formula is $$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$ .

The midpoint is $$M = \left(\frac{4 + (-6)}{2}, \frac{12 + 14}{2}\right) = (-1, 13)$$ .

The correct calculation is $$d = \sqrt{(3 - (-2))^2 + (-5 - 7)^2}$$ .

The coordinates are $$M = \left(\frac{-2 + 6}{2}, \frac{7 + (-5)}{2}\right) = (2, 1)$$ .

The Midpoint represents the point that is exactly halfway between two endpoints of a line segment.

The Distance Formula allows us to calculate the straight-line distance between two points in a coordinate plane.