Answer to Question #126496 in Analytic Geometry for Deborah

Question

1. Calculate the distance between the following pairs of points:
a. (3,4), (5,2)
b. (0,6), (4,0)

2. Calculate the distance between the points (b,3) and (-b,2).

Answer 1

The distance between two points $(x_1,y_1)\text{ and }(x_2,y_2)\text{ is }\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}.$ Using this distance formula we obtain:

1.a. The distance between (3,4) and (5,2) is $\sqrt{(5-3)^2+(2-4)^2}=\sqrt{4+4}=\sqrt{8}=2\sqrt{2}.$

b. The distance between (0,6) and (4,0) is $\sqrt{4^2+6^2}=\sqrt{16+36}=\sqrt{52}=2\sqrt{13}.$

2. The distance between the points $(b,3)\text{ and }(-b,2)\text{ is } \sqrt{(-b-b)^2+(2-3)^2}=\sqrt{4b^2+1}.$