Question

What is the distance between the following points:1) A (3,5) and B (3,6)2)C (-2,-3) and D = (-2,-6)3) E (-3,1) and F = (-3,-1)

Answer 1

The distance between two points is determined using the formula:

`D=\sqrt{((x_2-x_1)^2\text{ }+(y_2-y_1)^2)}`

This formula will be used in solving the given problem.

1. A(3,5) and B(3,6)

`\begin{gathered} x_1=3 \\ x_2=3 \\ y_1=5 \\ y_2=\text{ 6} \end{gathered}`
`\begin{gathered} D\text{ = }\sqrt{((3-3)^2\text{ }+(6-5)^2)} \\ =\text{ }\sqrt{0^2\text{ }+1^2} \\ =\text{ }√(1) \\ D=\text{ 1} \end{gathered}`

2. C(-2,-3) and D(-2,-6)

`\begin{gathered} D\text{ = }\sqrt{((-2-(-2))^2\text{ }+(-6-(-3))^2} \\ =\text{ }\sqrt{((0)^2\text{ }+(-3)^2)} \\ =\text{ }√(9) \\ D=\text{ 3} \end{gathered}`

3. E(-3,1) and F(-3,-1)

`\begin{gathered} D\text{ = }\sqrt{(-3-(-3))^2\text{ }+(-1-1)^2} \\ =\text{ }\sqrt{0^2\text{ }+(-2)^2} \\ =\text{ }√(4) \\ D=\text{ 2} \end{gathered}`