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