Answer:
x = 16 or -2
Step-by-step explanation:
If both lines are congruent, their magnitudes are equal.
To find the magnitude of a line, the equation to use is;
D = √(x2-x1)^2 + (y2-y1)^2
So for AB, we have
D = √(-2 + 11)^2 + (5 + 3)^2
D = √81 + 64 = √145
For the second line
The distance would be;
D = √x-7)^2 + (9-1)^2
D = √(x-7)^2 + 8^2
Equate both magnitude
√145 = √(x-7)^2 + 64)
Simply remove the square roots on both sides
145 = 64 + (x - 7)^2
145 -64 = (x -7)^2
81 = (x-7)^2
Thaw the square root of both sides
x - 7 = 9
or x -7 = -9
x = 9 + 7 or x = -9 + 7
x = 16 or -2
