Question

Find the distance between the points (-3,10) and (9,-6)

Answer 1

The distance between the two points would be 20

Answer 2

Answer:

20

Step-by-step explanation:

The distance formula is:

$d = \sqrt {\left( {x_1 - x_2 } \right)^2 + \left( {y_1 - y_2 } \right)^2 }$

where (x₁, y₁) and (x₂, y₂) are the points. We are given the points (-3,10) and (9,-6). Therefore,

$x_{1}=-3 \\y_{1}= 10\\x_{2}=9 \\y_{2}=-6$

Substitute the values into the formula.

$d = \sqrt {\left( {-3 - 9} \right)^2 + \left( {10- -6} \right)^2 }$

$d = \sqrt {\left( {-3 - 9} \right)^2 + \left( {10+6} \right)^2 }$

Solve inside the parentheses. Subtract 9 from 3. Add 10 and 6.

$d = \sqrt {\left( {-12} \right)^2 + \left( {16} \right)^2 }$

Evaluate the exponents.

⇒ -12²= -12*-12= 144

$d = \sqrt {\left144 + \left( {16} \right)^2 }$

⇒ 16²= 16*16=256

$d = \sqrt {\left144 + \left256}$

Add 144 and 256.

$d=\sqrt{400}$

Take the square root of 400.

$d=20$

The distance between the two points is 20.