monirjewel wrote:
Attachment:
Coordinate.jpg
In the rectangular coordinate system above the area of triangle PQR is what fraction of the area triangle LMN?
A. 1/9
B. 1/8
C. 1/6
D. 1/5
E. 1/3
Understanding the question: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)^2
What'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 =12
What is asked for:Area of PQR/Area of LMN => Ratio of the areas
Solution: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