Find x such that the point (x,4) is 10 units from (-2,-2)
distance formula comes to the rescue:
10^2=(x+2)^2+(4+2)^2
solve for x.
To find the value of x such that the point (x, 4) is 10 units away from (-2, -2), we can use the distance formula. The distance formula calculates the distance between two points in a coordinate plane:
Distance between two points (x1, y1) and (x2, y2) = sqrt((x2 - x1)^2 + (y2 - y1)^2)
In this case, we have the following points:
Point 1: (-2, -2)
Point 2: (x, 4)
Using the distance formula, we can set up the equation:
sqrt((x - (-2))^2 + (4 - (-2))^2) = 10
Simplifying the equation, we get:
sqrt((x + 2)^2 + 36) = 10
Next, let's square both sides of the equation to eliminate the square root:
(x + 2)^2 + 36 = 100
Expanding and simplifying the equation further:
x^2 + 4x + 4 + 36 = 100
x^2 + 4x + 40 = 100
Subtracting 100 from both sides:
x^2 + 4x - 60 = 0
Now we have a quadratic equation. To solve it, we can either factorize or use the quadratic formula. Let's factorize it:
(x - 6)(x + 10) = 0
Setting each factor to zero:
x - 6 = 0 or x + 10 = 0
Solving for x in both equations:
x = 6 or x = -10
Therefore, there are two possible values for x that satisfy the condition: x = 6 or x = -10.