Question

Calculate the distance between (4,9) and (-2,6) using the distance formula.

Answer 1

`\large\boxed{d=3\sqrt5}`

Explanation:

`\text{the formula of a distance between two points}\ A(x_1,\ y_1)\ \text{and}\ B(x_2,\ y_2):\\\\|AB|=√((x_2-x_1)^2+(y_2-y_1)^2)\\=========================\\\\\text{We have}\ (4,\ 9)\ \text{and}\ (-2,\ 6).\ \text{Substitute:}\\\\d=√((-2-4)^2+(6-9)^2)=√((-6)^2+(-3)^2)=√(36+9)=√(45)\\\\√(45)=√(9\cdot5)=\sqrt9\cdot\sqrt5=3\sqrt5`