What is the shortest distance between the points G and E?

Concept: Pythagoras' theorem — in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) equals the sum of the squares of the other two sides: hypotenuse2 = base2 + perpendicular2. This gives the straight-line (shortest) distance between two points once the perpendicular segments connecting them are known.

Application: In the given figure, G and F are joined by a vertical segment of 8 m, and F and E are joined by a horizontal segment of 6 m, so GF is perpendicular to FE, and triangle GFE is right-angled at F. The straight-line distance GE is therefore the hypotenuse of this right triangle: GE = √(GF2 + FE2) = √(82 + 62) = √(64 + 36) = √100 = 10 m.

Cross-check: The figure's own diagonal from G to E is directly marked as 10 m, independently confirming the computed value.

So the shortest distance between G and E is 10 m.