The length of the line joining points (x,4) and (-x,3) is 7 units. Find the value of x.
- 4√3
- 2√6
- 3√2
-
2√3
The correct answer is: D
Explanation
d = \(\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\)
x1 = x, x2 = -x, y1 = 4, y2 = 3, d = 7
7 = \(\sqrt{(-x -x)^2 + (3 - 4)^2}\)
7 = \(\sqrt{(-2x)^2 + (-1)^2}\)
7 = ( \(\sqrt{4x^2 + 1}\)
square both sides
7\(^2\) = 4x\(^2\) + 1
collect like terms
4x\(^2\) = 49 - 1
4x\(^2\) = 48
x\(^2\) = \(\frac{48}{4}\)
x\(^2\) = 12
x = √12
x = 2√3