OE


Draw the points and connect the points to form a right triangle. Subtract the x-coordinate of A from that of C to find the length of AC: 7 − 1 = 6. Subtract the y-coordinate of C from that of B to find the length of BC: $4 + 6 \sqrt{3}− 4 = 6$. Notice that the ratio of AC to BC is 1 to $\sqrt{3}$. Therefore, ABC is a 30-60-90 triangle, and the length of AB, the hypotenuse, will be double the length of the shorter side (6), so AB = 12. The absolute value of the difference will be the positive value, obtained by subtracting the smaller value (BC) from the larger value (the length of the hypotenuse, AB):$AB − BC = 12 − 6 \sqrt{3}$ , which is choice (E).