What kind of map is rectangular representation of Earth that shows accurate directions but distorts size ans distance?

Answer 1

ALL flat maps distort distances and directions. The Earth is roughly a sphere; there is no way to show a flat map without distortions. When you press your face against a window, flattening your face distorts your image; so too with every kind of map. The only map with no distortion is a globe.

But each different kind of map produces different kinds of distortions, so it's important to pick the kind of map that produces the least distortion for your purpose.

But perhaps the worst map, in terms of distortion at higher latitudes, is the Mercator projection of the entire Earth. Along the equator, a Mercator map is quite accurate, but as you move north or south of about 45 degrees latitude, it becomes wildly exaggerated.

For higher latitudes, choose a "conic section" matched to your latitude. Around the poles, you should choose a polar projection map.

Answer 2

Mercator projection