Question

Katy needs to go to the museum which is 50 feet northwest of her house. Her mother has taken the car keys and all other means of communication. The sidewalks are horizontal and vertical and she must stay on the sidewalk. What direction must mary travel to get to the museum. Assume that Katy's house is at the origin and the museum is her destination (point). Name the quadrant of the museum. Can someone please explain the answer

Answer 1

Figures in the plane

Katy must walk on the sidewalks, so she can reach the museum by going vertically and then to the west, or vice-versa

In any case, the total distance she must walk by is the sum of the sides of the triangle shown in the drawing

Since the direction of the museum is northwest, both distances are equal. We only have to calculate one of them and then multiply by 2

Let's call x to the distance by the sidewalk, the relation between them and the hypotenuse of the triangle is:

`x^2+x^2=50^2`

We have applied the Pythagoras Theorem

Joining like terms:

`2x^2=50^2`

Dividing by 2:

`x^2=(50^2)/(2)=(2500)/(2)=1250`

Solving for x:

`x=\sqrt[]{1250}=35.36`

The distance Katy needs to walk is 2x= 70.72 feet

The quadrant of the museum is the second or quadrant II