The length of the line joining points (x,4) and (-x,3) is 7 units. Find the

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