Question

What is the exact distance from (−1, 4) to (6, −2)?

Answer 1

Same as last time:

d^2=(x2-x1)^2+(y2-y1)^2

d^2=(6--1)^2+(-2-4)^2

d^2=7^2+(-6)^2

d^2=49+36

d^2=85

d=√85 (85=5*7 and both 5 and 7 are prime so √85 cannot be simplified any further)

The exact distance is √85 units.

Answer 2

The distance is √ 85 units

Explanation:

To find the exact value, all we will simply do is to use the distance formula to solve;

D =√ (x₂ - x₁)² + (y₂ - y₁)²

From the question given;

The points given are (−1, 4) and (6, −2)

so; x₁ = -1 y₁ = 4 x₂ = 6 y₂ = -2

We can now proceed to substitute the formula into the equation

D = √ (x₂ - x₁)² + (y₂ - y₁)²

=√ (6 - -1)² + (-2 - 4)²

=√ (6+ 1)² + (-2 - 4)²

=√ (7)² + (-6)²

=√ 49 + 36

=√ 85

The distance is √ 85 units