Answer :
Answer:
The distance between the two points is [tex]\sqrt{85}[/tex] units
Step-by-step explanation:
Let us revise the rule of the distance between two point [tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex]
[tex]d=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}[/tex]
∵ We need to find the distance between the two points (8, -7) and (1, -1)
→ Let [tex]x_{1}[/tex] = 8 and [tex]x_{2}[/tex] = 1
→ Let [tex]y_{1}[/tex] = -7 and [tex]y_{2}[/tex] = -1
→ Substitute their values in the rule above
∴ [tex]d=\sqrt{(1-8)^{2}+(-1--7)^{2}}[/tex]
∴ [tex]d=\sqrt{(-7)^{2}+(-1+7)^{2}}[/tex]
∴ [tex]d=\sqrt{49+36}[/tex]
∴ [tex]d=\sqrt{85}[/tex]
→ Simplify the radical
∵ 85 = 5 × 17
→ Both of them are prime numbers
∴ The simplest form of [tex]\sqrt{85}[/tex] is [tex]\sqrt{85}[/tex]
∴ The distance between the two points is [tex]\sqrt{85}[/tex] units