Answer:
20
Step-by-step explanation:
The distance formula is:
[tex]d = \sqrt {\left( {x_1 - x_2 } \right)^2 + \left( {y_1 - y_2 } \right)^2 }[/tex]
where (x₁, y₁) and (x₂, y₂) are the points. We are given the points (-3,10) and (9,-6). Therefore,
[tex]x_{1}=-3 \\y_{1}= 10\\x_{2}=9 \\y_{2}=-6[/tex]
Substitute the values into the formula.
[tex]d = \sqrt {\left( {-3 - 9} \right)^2 + \left( {10- -6} \right)^2 }[/tex]
[tex]d = \sqrt {\left( {-3 - 9} \right)^2 + \left( {10+6} \right)^2 }[/tex]
Solve inside the parentheses. Subtract 9 from 3. Add 10 and 6.
[tex]d = \sqrt {\left( {-12} \right)^2 + \left( {16} \right)^2 }[/tex]
Evaluate the exponents.
⇒ -12²= -12*-12= 144
[tex]d = \sqrt {\left144 + \left( {16} \right)^2 }[/tex]
⇒ 16²= 16*16=256
[tex]d = \sqrt {\left144 + \left256}[/tex]
Add 144 and 256.
[tex]d=\sqrt{400}[/tex]
Take the square root of 400.
[tex]d=20[/tex]
The distance between the two points is 20.
