Questions: A pair of points is graphed. (a) Find the distance between them. (b) Find the midpoint of the segment that joins them.

Solution Steps

The coordinates of the two points are:

• Point 1: (0, 1)
• Point 2: (1, 0)

Use the distance formula: \[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \] Substitute the coordinates: \[ d = \sqrt{(1 - 0)^2 + (0 - 1)^2} \] \[ d = \sqrt{1 + 1} \] \[ d = \sqrt{2} \]

Use the midpoint formula: \[ \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \] Substitute the coordinates: \[ \left( \frac{0 + 1}{2}, \frac{1 + 0}{2} \right) \] \[ \left( \frac{1}{2}, \frac{1}{2} \right) \]

Final Answer