Question

Find the distance between the two points in simplest radical form. (8, – 7) and (1, -1)

Answer 1

Answer:

The distance between the two points is $\sqrt{85}$ units

Step-by-step explanation:

Let us revise the rule of the distance between two point $(x_{1},y_{1})$ and  $(x_{2},y_{2})$

$d=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}$

∵ We need to find the distance between the two points (8, -7) and (1, -1)

→ Let $x_{1}$ = 8 and $x_{2}$ = 1

→ Let $y_{1}$ = -7 and $y_{2}$ = -1

→ Substitute their values in the rule above

∴ $d=\sqrt{(1-8)^{2}+(-1--7)^{2}}$

∴ $d=\sqrt{(-7)^{2}+(-1+7)^{2}}$

∴ $d=\sqrt{49+36}$

∴ $d=\sqrt{85}$

→ Simplify the radical

∵ 85 = 5 × 17

→ Both of them are prime numbers

∴ The simplest form of $\sqrt{85}$ is $\sqrt{85}$

∴ The distance between the two points is $\sqrt{85}$ units