Understanding the question:
In the rectangular coordinate system above the area of triangle PQR is what fraction of the area triangle LMN?
Two triangles are given. They look proportional/similar but this should be confirmed. Also, means are provided to calculate length of base and height.Facts to refer:
If 2 triangles are similar, then the ratio of their area= (ratio of the sides)^2What's given in the question and what it implies (noted as =>):
Coordinates for L, P, R, N are given => Base of smaller triangle = 4 and that of larger triangle =12
Coordinate for M and Q are given => Height of smaller triangle = 4 and that of larger triangle =12What is asked for:
Area of PQR/Area of LMN => Ratio of the areasSolution:
Since the base and height of the triangles are of the same ratio, the 2 triangles are similar. (Since the base and height are of equal ratio, the other 2 sides will also be of the same ratio.) Hence the fact given in "Facts to refer" can be used.
Ratio of sides = 4/12 =1/3
(Ratio of areas) = (1/3)^2 = 1/9