DistanceDetermine the distance from the point (- 5, 6 ) to the origin.

Expert Answers
justaguide eNotes educator| Certified Educator

The distance between two points (x1, y1) and (x2, y2) is given by sqrt[(x1 - x2)^2 + (y1 - y2)^2]

Here the point is (-5, 6) and the origin is (0, 0)

The distance between the two is sqrt[(-5 - 0)^2 + (6 - 0)^2]

=> sqrt (25 + 36)

=> sqrt 61

The required distance is sqrt 61

tonys538 | Student

If two points have coordinates (x, y) and (X, Y), the distance between the points is given by the formula D = `sqrt((X - x)^2+(Y-y)^2)`

Here, the distance of the point (-5, 6) from the origin is required. The origin has coordinates (0,0)

The required distance is `sqrt((0 +5)^2 + (0-6)^2) = sqrt(25 + 36) = sqrt 61`

The point (-5, 6) is `sqrt 61` units from the origin.

giorgiana1976 | Student

We'll form a right angle triangle, whose hypotenuse is the distance from origin to the point and one cathetus is its abscisa and the other cathetus is the ordinate.

We'll note the distance as r:

r = ? units.

We'll note the abscisa as x:

x = -5 units

x^2 = 25 square units

We'll note the ordinate as y:

y = 6 units

y^2 = 36 units

We'll calculate r using Pythagorean Theorem:

r^2 = x^2 + y^2

r^2 = 25 + 36

r^2 = 61

r = sqrt 61

r = 7.81 units approx

We'll reject the negative solution since the distance is always positive.