Respuesta :

Sarah06109

Answer:

[tex]\boxed {\boxed {\sf d=\sqrt{170} \ or \ d\approx 13.04}}}[/tex]

Step-by-step explanation:

We are asked to find the length of a segment or the distance between the 2 points. The formula for distance is:

[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 given the points ( -5, 4) and (6, -3). If we match the number and the corresponding variable, it is:

  • x₁= -5
  • y₁= 4
  • x₂= 6
  • y₂ = -3

Substitute the values into the formula.

[tex]d= \sqrt{(6--5)^2+(-3-4)^2[/tex]

Solve inside the parentheses.

  • 6--5 (Back to back negative signs become a positive)= 6+5 =11
  • -3-4= -7

[tex]d= \sqrt{(11)^2+(-7)^2[/tex]

Solve the exponents.

  • (11)²= 11*11= 121
  • (-7)²= -7*-7= 49

[tex]d= \sqrt {(121)+(49)[/tex]

Add.

[tex]d= \sqrt {170}[/tex]

[tex]d=13.0384048104[/tex]

Even though it's not specified, we could round to the nearest hundredth to make the answer more concise. The 8 in the thousandth place tells us to round the 3 to a 4 in the hundredth place.

  • 13.0384048104

[tex]d\approx 13.04[/tex]

The length of the segment is √170 or approximately 13.04.

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