The length of the line joining points (x,4) and (-x,3) is 7 units. Find the value of x.
Answer Details
The problem provides us with two points, (x, 4) and (-x, 3), and tells us that the distance between them is 7 units. We need to find the value of x that satisfies this condition.
To find the distance between two points, we can use the distance formula:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
where (x1, y1) and (x2, y2) are the coordinates of the two points, and d is the distance between them.
Using this formula, we can calculate the distance between the given points:
d = sqrt((-x - x)^2 + (3 - 4)^2)
d = sqrt(4x^2 + 1)
We are given that this distance is equal to 7 units:
sqrt(4x^2 + 1) = 7
To solve for x, we need to isolate it on one side of the equation. To do this, we will square both sides of the equation:
4x^2 + 1 = 49
Now we can solve for x:
4x^2 = 48
x^2 = 12
x = sqrt(12) = 2sqrt(3)
Therefore, the value of x that satisfies the given conditions is 2sqrt(3), which is option D.