Question

6. How far is it from the point (-5, 7) to the point (6,-2)? Round your answer to the nearest tenth.

Answer 1

Answer:

14.2 units

Step-by-step explanation:

Here x increases by 11 from -5 to +6.  This is the length of the horizontal leg of a right triangle.  Then y decreases by 9 from 7 to -2.  This is the length of the vertical leg.  The hypotenuse of this triangle may be found using the Pythagorean Theorem:

11^2 + 9^2 = (hypotenuse)^2, or

hypotenuse = √(121 + 81) = √202 ≈ 14.2 units

Answer 2

Answer:

≈ 14.2

Step-by-step explanation:

Calculate the distance d using the distance formula

d = $\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }$

with (x₁, y₁ ) = (- 5, 7) and (x₂, y₂ ) = (6, - 2)

d = $\sqrt{(6+5)^2+(-2-7)^2}$

  = $\sqrt{11^2+(-9)^2}$

  = $\sqrt{121+81}$

  = $\sqrt{202}$

  ≈ 14.2 ( to the nearest tenth )