Question

Use the coordinate plane to estimate the distance between the two points. Then use the distance formula to find the distance between the points. Round the result to the nearest hundredth. \((-3,-2),(4,1)\) \((0,0),(20,0),(20,21)\)

Short answer

The distance between points (-3,-2) and (4,1) is 7 units, and the distance from (0,0) to (20,21) is 29 units.

Step-by-step solution

Estimate the Distance Between Points

By sketching the points on the coordinate plane and drawing a straight line between them, get a visual representation of the approximate distance between the points.

Calculate the Distances Using the Distance Formula

Plug the coordinates into the distance formula, \(\sqrt{{(x_2-x_1)}^2 + {(y_2-y_1)}^2}\), and calculate. For the points (-3,-2) and (4,1), this results in \(\sqrt{{(4 - (-3))}^2 + {(1 - (-2))}^2} = \sqrt{{49}} = 7\). For the points (0,0) and (20,21), this results in \(\sqrt{{(20 - 0)}^2 + {(21 - 0)}^2} = \sqrt{{841}} = 29\).

Check Your Work and Round off to Nearest Hundredth

The calculated distances are already exact, so there's no need to round. Compare your results with the estimations from Step 1 to confirm they're reasonable.