Question

Find the distance between (2a+2, 2b) and (2b+2, 2a), given that a>b.

Answer 1

Answer:

Distance = $2\sqrt{2}a-2\sqrt{2}b$

Step-by-step explanation:

We will use distance formula shown below to solve this:

Distance Formula:  $\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}$

Where

x_1 = 2a + 2

y_1 = 2b

x_2 = 2b+2

y_2 = 2a

Substituting, we solve for the expression for distance:

$D=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}\\D=\sqrt{(2a-2b)^2+((2b+2)-(2a+2))^2}\\D=\sqrt{(2a-2b)^2+(2b+2-2a-2)^2}\\D=\sqrt{(2a-2b)^2+(2b-2a)^2}\\D=\sqrt{4a^2 -8ab+4b^2+4b^2-8ab+4a^2}\\D=\sqrt{8a^2-16ab+8b^2}\\D=\sqrt{(2\sqrt{2}a-2\sqrt{2}b)^2}\\D=2\sqrt{2}a-2\sqrt{2}b$

This is the expression in terms of a, and b,  given a > b