Final answer:
An angle in standard position with its terminal side passing through (5, -2) is drawn from the origin through the point. The distance from the origin to this point is calculated using the Pythagorean theorem, which yields a distance of √29.
Step-by-step explanation:
To draw an angle in standard position whose terminal side contains the point (5, −2), you would start by drawing a coordinate system (x- and y-axes). Then plot the given point and draw a ray from the origin (0,0) through the point (5, −2). This ray represents the terminal side of the angle in standard position.
To find the distance from the origin to this point, you use the Pythagorean theorem. The distance d can be calculated using the formula d = √(x² + y²), where x and y are the coordinates of the point. For the point (5, −2), the calculation is d = √(5² + (−2)²) = √(25 + 4) = √29, which is the distance from the origin to the point (5, −2).