Question

why might it be easier to use the distance formula to find the distance between the points (-245, 500) and (312, 61) instead of the pythagorean theorem and a graph? we cant use the pythagorean theorem when one of the points contains a negative x - value. it is not possible to sketch a right triangle with these points as two of the vertices. plotting these points on a graph might be tough to do since they are so far away from the origin.

Explanation:

• For the first option: The Pythagorean theorem can be used with negative x - values (we use the absolute difference for the horizontal leg), so this is incorrect.
• For the second option: We can always sketch a right triangle with two points as vertices (by drawing horizontal and vertical lines from the points to form the legs), so this is incorrect.
• For the third option: The points \((- 245,500)\) and \((312,61)\) have large - magnitude coordinates. Plotting them accurately on a standard graph (which typically has a limited range around the origin) would be difficult. The distance formula \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\) can be used directly with the coordinates without the need for plotting, making it easier in this case.

Answer:

C. Plotting these points on a graph might be tough to do since they are so far away from the origin.