Determine the values of x and y when given the distance ( x;-3) from the origin is 5 units

Answer 1

To find the values of x and y when the distance from the origin is 5 units, we can use the distance formula in two dimensions, which is:

Distance = √(x^2 + y^2)

Given that the distance from the origin is 5 units, we can substitute this into the formula and solve for x and y:

5 = √(x^2 + (-3)^2)
5 = √(x^2 + 9)
25 = x^2 + 9
x^2 = 16
x = ±4

Therefore, the values of x can be either 4 or -4. To find the corresponding values of y, we can substitute the values of x into the equation for the distance from the origin:

If x = 4:
5 = √(4^2 + y^2)
5 = √(16 + y^2)
25 = 16 + y^2
y^2= 9
y = ±3

Therefore, if x = 4, y can be either 3 or -3.

If x = -4, following the same steps:
5 = √((-4)^2 + y^2)
5 = √(16 + y^2)
25 = 16 + y^2
y^2= 9
y = ±3

Therefore, if x = -4, y can also be either 3 or -3.

In conclusion, the two possible solutions for the values of x and y when the distance from the origin is 5 units are:
1. (4, 3) and (4, -3)
2. (-4, 3) and (-4, -3)