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This is a question on plane geometry and involves Pythagorastheorem. The ant finishes at a point which we will call point C. You have created a right angle triangle. As we know the length of two of the sides we can calculate the third with the theorem. The theorem is "the square on the hypotenuse of a right angled triangle is equal to the sum of the square on the other two sides". That may sound complex but it is not, work it out like this.

One side of the triangle is 6cm so you square this number (multiply it by itself 6 x 6) = 36.

The other side is 8cm so you do the same (8 x 8) = 64. Then add the two together.

36 + 64 = 100. You then need to find the square root of this number. In this case it is 10.

So the distance traveled is 6 + 8 = 14cm and the displacement from the original point is 10cm

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