### Video Transcript

Maps of the world use a coordinate system to represent locations where the horizontal axis is the equator and the vertical axis is the prime meridian. Where does 45 degrees north latitude, 20 degrees east longitude lie? Where does 10 degrees north latitude, 10 degrees west longitude lie?

To make things a little clearer on our map, we can begin by highlighting our horizontal and vertical axes, that is, the equator and the prime meridian. The horizontal lines in our coordinate system are called the lines of latitude. And each line of latitude runs east to west and measures the number of degrees north or south of the equator. The lines of longitude, on the other hand, run north to south, and these measure the number of degrees east or west of the prime meridian.

Now, in a coordinate system, the position of any point 𝑀 is specified by its coordinates; that’s the ordered pair 𝑥 sub 𝑀, 𝑦 sub 𝑀. In our case, 𝑥 sub 𝑀 is the number of degrees on the horizontal axis at the point of intersection of the line parallel to the vertical axis — that’s the prime meridian — and through 𝑀. So, 𝑥 sub 𝑀 corresponds to the longitude. Similarly, 𝑦 sub 𝑀 is the number of degrees on the vertical axis. That’s the prime meridian at the point of intersection of the line parallel to the horizontal axis or the equator and through the point 𝑀. And so, 𝑦 sub 𝑀 represents the latitude.

Now in the first part of the question, we’re given the coordinates. 45 degrees north is the latitude, and 20 degrees east is the longitude. And this means that 𝑥 sub 𝑀 is 20 degrees east and 𝑦 sub 𝑀 is 45 degrees north. And these make up our ordered pair. We can sketch a line through 20 degrees east on the equator and parallel to the prime meridian. So, this is the longitude of our point. And similarly, we can sketch a line through 45 degrees north on the prime meridian and parallel to the equator. And that’s our latitude. And where the two lines meet is the position of the point. So, 45 degrees north latitude, 20 degrees east longitude lies in Europe.

Now, similarly, for the second part, we have 10 degrees north latitude and 10 degrees west longitude. And so, our point has the coordinates 𝑥 sub 𝑀 is 10 degrees west and 𝑦 sub 𝑀 is 10 degrees north. And on our map, we can draw a vertical line through 10 degrees west on the equator and a horizontal line through 10 degrees north on the prime meridian. And we see that the lines meet at a point in Africa.

Our answers then are for part one 45 degrees north latitude and 20 degrees east longitude lies in Europe and part two 10 degrees north latitude and 10 degrees west longitude lies in Africa.