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

≈ 14.2

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 =
`√((6+5)^2+(-2-7)^2)`

=
`√(11^2+(-9)^2)`

=
`√(121+81)`

=
`√(202)`

≈ 14.2 ( to the nearest tenth )

Answer 2

14.2 units

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