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. \((5,-2),(-1,1)\) \((0,0),(20,0),(20,21)\)

Short answer

The distance between the first pair of points is 6.71, while the distance of the second set of points is 41.

Step-by-step solution

Identify the Points

The first part of the problem is to identify the coordinates of the points. So, the coordinates of the first two points are (5,-2) and (-1,1). The coordinates of the second set of points are (0,0), (20,0) and (20,21).

Compute for the First Pair

Now, apply the formula \(\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\) for the first pair of points. Substitute the values \(\sqrt{((-1) - 5)^2 + (1 - (-2))^2}\), which simplifies to \(\sqrt{((-6)^2) + ((3)^2)}\) = \(\sqrt{36 + 9}\) = \(\sqrt{45}\). Finally, round the result to the nearest hundredth equals 6.71.

Compute for the Second Set of Points

For the second set of points, find the distance from (0,0) to (20,0) which equals to \(\sqrt{(20 - 0)^2 + (0 - 0)^2}\) = \(\sqrt{(20)^2}\) = \(20\). Then, find the distance from (20,0) to (20,21) which equals to \(\sqrt{(20 - 20)^2 + (21 - 0)^2}\) = \(\sqrt{(0)^2 + (21)^2}\) = \(21\). Hence, the total distance is \(20 + 21 = 41\).