Answer:
[tex]\boxed {\boxed {\sf d= \sqrt{34}}}[/tex]
Step-by-step explanation:
We want to find the distance between two points, so the following formula is used.
[tex]d= \sqrt{(x_2-x_1)^2+(y_2-y_1)^2[/tex]
Where (x₁, y₁) and (x₂, y₂) are the points we are finding the distance between.
We are given the points (-2, -1) and (3,2). If we match the corresponding value and variable we see that:
Substitute the values into the formula.
[tex]d= \sqrt {(-2-3)^2+(2--1)^2[/tex]
Solve the parentheses.
- -2 -3 = -5
- 2--1 = 2+ 1 = 3
[tex]d= \sqrt{(-5)^2+(3)^2[/tex]
Solve the exponents.
- (-5)²= -5*-5= 25
- (3)²= 3*3=9
[tex]d= \sqrt{25+9}[/tex]
Add.
[tex]d= \sqrt{34}[/tex]
This radical cannot be simplified, so the distance between the two points is √34 and choice 3 is correct.
