the coordinates a(5, -2), b(3,-1),c(-4,-4) d(-3,8) and e(-1,4) forms the vertices of the polygon when they are connected in order.
in order to classify that which polygon is it with the given coordinates, first count the number of vertices and then count the number of sides it can make with these vertices.
since, the given coordinates have five vertices, therefore, it will make five sides. moreover, pentagon is regular in nature therefore it will be convex.
now, a polygon with five sides is known as pentagon, therefore, the given polygon is the pentagon.
given that there are two triangles j'k'l' and jkl>
the former is got by dilating the second one.
when drawn on a grid, (graph paper) coordinates of vertices of first triangle is
(6,12)j, (9,6)k and (12,9)l
side jk has length = distance between j and k
side j'k'=distance between j' and k'
ie j'k'l' has sides 1/3 of that of corresponding sides of jkl.
hence scale factor of 1/3 is used to get j'k'l'from jkl