The scale of a map says that 4 cm represents 5 km. a. What distance on the map (in centimeters) represents an actual distance of 4 kilometers?

cm represents the actual distance of 4 kilometers.

b. What is the actual number of kilometers that is represented by 5 centimeters on the map?

5 cm represents
km

i think its a.

hope this

isocolese triangle

we know that the line connect a and b is the hyptonuse

so first find the hypotonuse length using the distance formula, call the length c

since it is an isocolese triangle, the lengths of the legs are the same

using pythagorean theorem,

in this case, a=b since isocolese triangle so we get

or

we can find c so we can find the distances

we know that if we draw 2 circles, each has center at a and b, and find where they intersect, we can the 2 possible locations for c

if a has center at (xa,ya) and b has center at (xb,yb), then we can solve where

and

intersect to find where they intersect

i'm not going to put an example because i have to go to class. i hope this explanation is enough