Find the shortest distance from a to c in the diagram below.

The shortest distance from A to C is

Step-by-step explanation:

see the attached figure to better understand the problem

we know that

The shortest distance from A to C is the hypotenuse of the right triangle AYC

Applying the Pythagoras Theorem

step 1

Find the length YC (hypotenuse of the right triangle YBC)

Applying the Pythagoras Theorem

substitute the given values

step 2

Find the shortest distance from A to C

substitute the given values

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step-by-step explanation:

let pq = qr = rs = x, and xz = y and zu = z.

if the horizontal lines are parallel, then corresponding segments are in proportion:

substitute:

therefore 3 = y = z.

xu = y + z → xu = 3 + 3 = 6