Question

Find the shortest distance from A to C in the diagram below.

Answer 1

The shortest distance from A to C is
`AC=5√(13)\ units`

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

`AC^(2)=AY^(2) +YC^(2)`

step 1

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

Applying the Pythagoras Theorem

`YC^(2)=YB^(2) +BC^(2)`

substitute the given values

`YC^(2)=6^(2) +15^(2)`

`YC^(2)=261`

`YC=√(261)\ units`

step 2

Find the shortest distance from A to C

`AC^(2)=AY^(2) +YC^(2)`

substitute the given values

`AC^(2)=8^(2) +√(261)^(2)`

`AC^(2)=325`

`AC=√(325)\ units`

`AC=5√(13)\ units`