Introduction of Cartesian coordinate system

Let us study about cartesian coordinate system,
The Cartesian coordinate system was developed by the mathematician Descartes during an illness. As he lay in bed sick, he saw a fly buzzing around on the ceiling, which was made of square shaped tiles. As he watched he realized that he could describe the position of the fly by the ceiling tile he was on. After this experience he developed the coordinate plane to make it easier to describe the position of objects.

one of the coordinates in a system of coordinates that locates a point on a plane or in space by its distance from two lines or three planes respectively; the two lines or the intersections of the three planes are the coordinate axes.

I hope the above explanation was useful.

Proportional Parts of Similar Triangles

Let us learn about proportional parts of similar triangles,

Theorem : If two triangles are similar, then the ratio of any two corresponding segments (such as altitudes, medians, or angle bisectors) equals the ratio of any two corresponding sides.

In Figure 1, suppose Δ QRS∼ Δ TUV.

Figure 1 Corresponding segments of similar triangles.

Then,

Then, according to Theorem,

Example 1: Use Figure 2 and the fact that Δ ABC∼ Δ GHI. to find x.

Figure 2 Proportional parts of similar triangles.

Hope the above explanation helped you.