Respuesta :

Answer:

[tex]\boxed {\boxed {\sf d= 13}}[/tex]

Step-by-step explanation:

Distance can be calculated using this formula:

[tex]d= \sqrt {(x_2-x_1)+(y_2-y_1)[/tex]

where (x₁, y₁) and (x₂, y₂) are the points. We are given the points (6, -9) and (1, 3). Therefore:

[tex]x_1= 6\\y_1= -9 \\x_2= 1\\y_2=3[/tex]

Substitute the values into the formula.

[tex]d= \sqrt {(1-6)^2+(3--9)^2[/tex]

Solve inside the parentheses.

  • 1-6= -5
  • 3--9= 3+9 = 12

[tex]d= \sqrt{(-5)^2 + (12)^2[/tex]

Solve the exponents.

  • (-5)²= -5*-5 =25
  • (12)²= 12 *12= 144

[tex]d= \sqrt { 25+144}[/tex]

Add and take the square root.

[tex]d=\sqrt{169} \\d= 13[/tex]

The distance is 13.

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