Answer:
[tex]\Huge\boxed{\mathsf{\Rightarrow \sqrt{205}}}}[/tex]
Step-by-step explanation:
The distance between the give points of (-16, -15) and (-2, -18).
First, use slope formula.
SLOPE FORMULA:
[tex]\Rightarrow \displaystyle \mathsf{\frac{Y_2-Y_1}{X_2-X_1} }}[/tex]
[tex]\Rightarrow \displaystyle \mathsf{\sqrt{(X_2-X_1)^2+(Y_2-Y_1)^2}}}[/tex]
[tex]\displaystyle \mathsf{\sqrt{\left(-2-\left(-16\right)\right)^2+\left(-18-\left(-15\right)\right)^2}}}[/tex]
Solve.
[tex]\displaystyle \mathsf{\sqrt{\left(-2+16\right)^2+\left(-18+15\right)^2}}}[/tex]
Add & subtract the numbers from left to right.
[tex]\displaystyle \mathsf{(-2+16)^2}}[/tex]
[tex]\displaystyle \mathsf{-2+16=14}}[/tex]
[tex]\displaystyle \mathsf{14^2}}[/tex]
[tex]\displaystyle \mathsf{(-18+15)^2}}[/tex]
[tex]\displaystyle \mathsf{-18+15=3}}[/tex]
[tex]\displaystyle \mathsf{=3^2}}[/tex]
[tex]\displaystyle \mathsf{\sqrt{14^2+3^2}}}[/tex]
Solve by exponent.
14²=14*14=196
√196+3²
3²=3*3=9
√196+9
Add.
√196+9=205
√205
[tex]\Large\boxed{\mathsf{\Rightarrow \sqrt{205}}}}[/tex]
So, the correct answer is √205.
