Answer:
[tex]\boxed {\boxed {\sf d=10}}[/tex]
Step-by-step explanation:
The distance between two points can be calculated using the following formula.
[tex]d= \sqrt{(x_2-x_1)^2+(y_2-y_1)^2[/tex]
In this formula, (x₁, y₁) and (x₂, y₂) are the two points. We are given the points (-9, -2) and (-3,6). If we match the value with the corresponding variable we see that:
- x₁= -9
- y₁= -2
- x₂= -3
- y₂= 6
Substitute the values into the formula.
[tex]d= \sqrt {(-3 - -9)^2 + (6 - -2)^2[/tex]
Solve inside the parentheses. Remember that 2 back to back negative signs become a plus sign.
- (-3 - -9)= (-3+9)= 6
- ( 6- -2)= (6+2) =8
[tex]d= \sqrt{ (6)^2 + (8)^2[/tex]
Solve the exponents. Multiply the number by itself.
- (6)²= 6*6= 36
- (8)²= 8*8= 64
[tex]d= \sqrt{(36)+(64)[/tex]
Add.
[tex]d= \sqrt{100[/tex]
Take the square root of the number.
[tex]d= 10[/tex]
The distance between the points (-9, -2) and (-3, 6) is 10.
