Question

1. what does the distance formula calculate? a. the midpoint between two points b. the angle between two points c. the area between two points d. the straight - line distance between two points 2. what is the first step in deriving the distance formula from the pythagorean theorem? a. solve for one variable b. calculate the hypotenuse c. draw a circle d. plot the points and form a right triangle 3. if angle p and angle r are opposite angles in an inscribed quadrilateral and angle p = 120 degrees, what is angle r? a. 120 degrees b. 60 degrees c. 240 degrees d. 30 degrees

Explanation:

1. The distance formula $\text{d}=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$ calculates the straight - line distance between two points $(x_1,y_1)$ and $(x_2,y_2)$.
2. To derive the distance formula from the Pythagorean theorem, we first plot the two points and form a right - triangle with the line segment between the points as the hypotenuse.
3. In an inscribed quadrilateral, opposite angles are supplementary (their sum is 180 degrees). Given $\angle P = 120^{\circ}$, then $\angle R=180 - 120=60^{\circ}$.

Answer:

1. d. The straight - line distance between two points
2. d. Plot the points and form a right triangle
3. b. 60 degrees